I will confess that I only read the OP and then replied - so sorry if we're way off topic
For me, I played the 'wait for his initiation game' and for my guy, it was shocking. He initiated at first, but then waited for me to initiate contact after that. So, he didn't get much contact and sorta left 'us' alone for a bit - cos he didn't want to seem like he was hounding me.
In the past, I've only ever dated guys I was friends with (after High School, I found most of my friends ended up being male), so there was no problem if I chose to IM, SMS them (or whatever) - it was generally a catch up, hi how you going kinda thing. I tend to take most of my relationships as 'friends first and foremost', so initiating the phonecall/SMS/IM was never viewed on negatively for them. Of course, if all the messages were 'I miss you's, where are you, I love you, etc etc' - I wouldn't blame them if they got irritated (same as if I'd sent 20 in 2 hours with no response - AKA How to Lose a Guy in 10 Days). I guess it all depends on the context of the chat, and whether you are also friends before you started dating.
It all depends on the guy - which is so frustrating! Some guys get offended if the girl initiates anything, especially in the Christian community, whereas most nowadays will chase once or twice, and then see how the girl reacts. If she then invites him somewhere - bingo! You got one (to sound rather uncouth)! If she doesn't -nope, not interested at all.
In this day and culture, fair is fair. You like someone - you interact with them - regardless of gender. A guy does not usually feel 'demasculinised' if a girl invites him somewhere and a girl does not lose her 'femininity' if a guy accepts her invite. If you like someone - start spending time with them! It isn't THAT hard...
If I get on well with a guy - I used to invite them to the movies for a night - I never saw it as a date, just friends hanging out having a good time, like I would with my girl friends.
Now that I have started dating someone, I have curbed that somewhat (we'll usually go out as a group or something), but he doesn't feel irritated if I ask him out - he likes it!! I've invited him to coffee, movies, pretty much everything...
It doesn't change the 'leadership' role of a relationship - guys like to be spoiled and taken out just as much as girls do! My ex used to complain that I never took him out and took initiative - it was something I had to learn to do (once I had enough money to do it)!
Sasch