An interesting question that I'm sure many of us have pondered before (but been to afraid to ask about). I remember first hearing about the possibility that they could have had sex in a discussion related to Paradise Lost--before then I had assumed the answer was no because I was so used to taking the Bible absolutely literally. "And the man and his wife were both naked but had no shame" is a phrase that I now understand has a lot of poetic meaning and symbolism--it's a polite euphemism to explain the marital union (sex within marriage with pleasure as the first goal and procreation as a possible bonus). So yes, I definitely believe that they probably had sex at least once. Sex is not a post-Fall aspect of life, and I think the Bible was trying to indicate that.
One interesting take I've heard on it is from John Walton's book, the Lost World of Adam and Eve. Walton makes tons of hypotheses regarding the Genesis account (with evidence to back them up), and for this particular section, he argues that Adam and Eve had sex just outside of the garden rather than inside it. The reason for this was that the Garden is meant to serve as an idealized, natural version of the Tabernacle--with an outer and inner section of "sacred space", as he calls it, with Adam and Eve serving as priests. His reasoning is that this is what is depicted in the Book of Jubilees--Adam and Eve have sex outside the garden, and then purify themselves before entering--and so that is how the ancient Jews interpreted that portion of the book.
Even if it is true that that is how it is in Jubilees, and it would make sense considering that sexual relations and even just an emission of sperm are considered "ritually impure" in the OT laws, I don't think it's necessarily true that Adam and Eve "had to" have sex outside the Garden. The Song of Solomon not only celebrates sex within a married context (contrary to what some other people claim), but the fact that sex has a whole book dedicated to it in the Biblical canon shows that's it's significant and not seen by God as some gross thing--otherwise He would not have inspired the ancient Jews to put it into their canon, if it was just a simple poem read at marriages. Prior to sin entering the world, sex was not impure at all and God would delight in their pleasure--not as a voyeur watching his creations in a inappropriate contentographic sense, but as a craftsman satisfied that His work fits together so well. Why it would not be allowed in the tabernacle later on is obvious--the sin-prone Israelites would not be able to control themselves sexually. Even if it was limited to the high priest and his wife, any sort of permission of sex in this sacred space would likely devolve into an orgy, or worse yet be seen as the thing being worthy of worship rather than the Creator who made it. This is what happened with the bronze serpent--it was a creation that was seen as the source of healing when that was the creator. Think about how sexualized our society is today--we worship sex and forget the God who made it, and Satan lies to us and says that God does not want us to have any kind of sexual pleasure. Many people, Christians included, have fallen for this lie. Abstinence and celibacy are a calling many people may have, of course, and their relationship with God is not damaged by never having sex. But for those who are called into a marriage, it's important to remember this.
