Well, I think physically you would have to fall asleep after a certain number of days (your brain just 'shuts down' basically at some duration of sleep deprivation, from what I understand). But if you just mean, bad enough you have extreme trouble sleeping (like for whole nights), than I have read of some other people who have had that, yeah.
Personally I haven't had it that bad, though tinnitus has been a motivating force for me to have a better sleep schedule now. If I follow that new sleep schedule (which has me not go to bed unless I'm sufficiently tired, for example), then I can fall asleep as quickly as I did 'when the world was quiet'. (which I'm very glad of)
Apparently some people use sleeping aids. I've never tried them so I can't comment on how well they work. (other than to say that from what I've read, it can help get you to sleep, but it has some unpleasant side effects like leaving you drowsy and sometimes raising the intensity of your tinnitus the morning after)