I think it all depends on who is next door. If they have children with them you are more likely to probably hear noise. On our first cruise we did NOT have connecting rooms, but every night at around 3 or 4 o'clock we would hear a girl whining about something (couldn't tell what she was saying) and a father yelling back to her, "You are 8 years old! You shouldn't be acting like this." and so on and so on.....this was EVERY night on our 4 night cruise. I don't know was wrong with the girl, but she had to wake up everyone every night.
Again this was NOT a connecting room, just the room behind us (on the other side of the back wall).
That is the only cruise we have every had problems with hearing other people in our room. We have been on 3 other cruises since then (but no connecting rooms) and all has been fine.
So, even without a connecting room, it is possible to hear the people next to you if they are really loud!
DJ