K.E.
My two boys (almost two years apart) have been sharing a room at night since the younger one was about 6 months old (the boys are now 2 and 4). However, I have never attempted to have them nap together. I don't know for sure, but I doubt it would work. I think they'd just play or talk. I put one of them down in a Pack n' Play in my bedroom and the other in their own bedroom. Now that my older one can be trusted not to fall off the couch (and now that he recognizes when he is tired and actually wants to take a nap), he sleeps on the couch when he naps (not every day), and the 2-year-old gets to use their bedroom.
My advice would be to start them off sharing the room at night rather than for naps because nighttime is when we sleep more soundly and are less likely to wake up. If we do wake up, we're more likely to fall back asleep. I know if one of my kids wakes up from a nap (because of a poopy diaper, sudden stop of the car, loud noise, etc.), even if the nap was much too short, there is no chance he is going to go back to sleep, however much he might need to.
Another thing to keep in mind is that, at only 3 months, your baby probably doesn't actually need a separate room for a nap. I have a 5-month-old who currently takes his naps in various places in the afternoon. Right now he's in his cosleeper in my bedroom, but often he sleeps on the changing table or a blanket on the floor. He probably won't need a separate space for a couple of months yet. Right now he just doesn't notice any distractions. I had both of my older sons nap in noisy environments when they were babies, and now they're both really good sleepers -- it takes a lot to wake them up (even though the middle one started out as a light sleeper, but I guess we got him used to noises).
When it gets time to move your kids to the same room at night, you might be surprised at how easy it is. I was nervous about it because my middle son did not sleep through the night yet, and he cries really loudly and persistantly. But my older son hardly ever woke up, and if he did, he always went right back to sleep. Now that both boys are talking and like to chat at night, we find it useful to put them to bed at different times (which works well when only one of them has napped -- the 4-year-old is ready for bed first).