It's very possible, but Scripture does not say.
We stay in our homes even when the day is really nice outside. Sometimes we want privacy or place to call our own that we can relax in. Not sure if you ever owned a home before, but if you did, you would know the value of relaxing inside the home vs. relaxing outside. Maybe one does not want to be disturbed and they want to study God's Word or pray in private. To assume we will have no privacy from other believers is a large assumption that the Scripture does not make. The fact that the Bible says that we have mansions means we will have mansions (Which most likely means some level or privacy from others). It may seem good to you, but it is written:
“But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11:6).
Well, privacy, will we have privacy? I thought part of the tradeoff of there not being marriage was that relationships with EVERYONE would be very intimate, beyond marriage intimacy (that's always the advertisement for how the tradeoff is "better"). Personally, I've thought it's a little bit of a copout, that people say that we'll be "more intimate" even when there is no marriage and no sex, which is as intimate as you can get in this life, to be one flesh, live together, and be a constant companion together, where there (at least shouldn't be) any secrets kept from each other (well outside of maybe keeping secret a present you want to give them), nor really any privacy, they would know everything about you ideally. If relationships in heaven, between everyone, are truly "more intimate" then that'd basically mean no privacy, maybe even to the point of reading minds. Because boy oh boy do people love to claim it'll be more intimate, I say "handshakes and side hugs are not more intimate than sex, they're gestures deliberately designed to limit intimacy" and people say "well we'll be SPIRITUALLY intimate" and I often wonder if they truly know that they want that between each and every person, to know every thought they've had, to delve into their darkest memories and even know of all their sins. Think about this, if it were not sin to have sex with anyone, and there were no disease, and you didn't have to worry about pregnancy, would you just up and have sex with anyone and everyone? Probably not, sexual intimacy is putting yourself in a vulnerable place with someone, we all have limitations on how close we want to be with other people, and that is how God designed it, promiscuity may be promoted to the world today as people make sex to be nothing but a cheap physical thrill, blaspheming what God originally made it to be, but ideally, it brings you to a closeness with someone that takes down all your walls and exposes yourself to that other person, it should only happen with a great amount of trust in that person.
Now if you wouldn't want to be sexually intimate with every single Christian you encountered, would you
really want to be spiritually intimate with them beyond a level of sexual intimacy, where you don't just know their body, but you know their spirit, their innermost thoughts, their memories, with no barriers between you, would you really want to have the memory of a Christian who'd been sexually abused as a child as if it were your own memory? Would you really want to know every thought that a former pedophile had before they found Christ? Our own sins are darkness enough than to have to experience what Jesus has experienced in knowing the sins of everyone ever born on earth. So unless we have no memories of what happened on earth while we were alive, some things I think would be best not knowing about other people, and best not shared with others, but kept between Jesus and ourselves, to which we can only say "Thank you for forgiving me for that and for taking my punishment for me, I'm sorry that I did it and caused the one I love most pain He did not deserve"
So.. yeah, I suppose at least from my point of view now, on this earth, in this body, I can see a need for privacy. But in many Christian's theology, there will not be any room for privacy, and I wonder if they themselves realize this.
That said.. do you really think we'll still be reading the bible in eternity when we have Jesus present with us living among us to receive His word directly from Him rather than reading a book that was put pen to paper by human authors (so second hand, yes it's Inspired but just like there are differences between the 3 synoptic gospels, each human being has their own way of using language and in some cases people can interpret things differently, the 3 synoptic gospels don't always quote Jesus word for word), and then translated, and then translated from that translation..... why not just hear from God directly? Not to mention there will be new things that God will say, rather than just the same story we've already read and at that time may already be fulfilled. On the same note, will we pray when we will be able to just... talk with God?
There is no marriage in Heaven because one will be like the angels in Heaven; But in the New Earth, they will be resurrected after the likeness of Christ. Jesus even alluded to the two different resurrections when He spoke to the Sadducees.
29 “Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God.
30 For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.
31 But as touching the resurrection of the dead, have ye not read that which was spoken unto you by God, saying,
32 I am the God of Abraham, and the God of Isaac, and the God of Jacob? God is not the God of the dead, but of the living.” (Matthew 22:29-32).
The words in red above is in reference to the resurrection of receiving a spiritual body like that of angels (Whereby there is no marriage). The words in blue above is in reference to the flesh and blood body resurrection that takes place in two phases (i.e. One in the Millennium, and the other for the New Earth after the Millennium and the Judgment). Seeing we will be in a different location like on Earth, and we will have flesh and blood bodies again, logic dictates that we could very well marry and have families there.
While I hope you're right because it has never made sense that God created marriage, a good thing, and male and female, only to just be temporary and just throw them away in the new earth and declare that whether you're male, or female, a male God is now your intimate spouse level relationship and that's it. Makes me think why create women and why declare homosexuality an abomination if sex itself is supposed to symbolize our relationship with Christ and, for many of us.. that would be a male-male relationship
BUT.. the scripture itself says in the Resurrection, so.. physical resurrection, no marriage, is the best we've gotten out of scripture, and Paul treats it like we're all being betrothed to the same husband in Jesus Christ. Which leads to THE most uncomfortable subject in Christianity for me. The idea that my desires for intimacy with a female have to be met by a male.
So as far as I know from scripture, these mansions, will be bachelor pads, that really don't have a purpose.
Hard to grasp we are that important huh 
