I hate to chime in with a negative, but here's my feeling...
I play a game to escape the real world, the pressures, the stress, and enjoy an all encompasing story that lets me forget I can't really swing a sword or take a full-on cannon burst to the chest. If I were playing a game that expected me to factor in real world time, I don't think I would find appreciation in that.
Another point I would make... If it were my game, I would find ways to KEEP people playing... obviously you're not TRYING to make them leave the game, but say if I DID stop at an Inn... and I needed healing desperately. I would feel pretty darn aggrevated if I knew I had to turn your fabulous game off for at least four hours when that darn evil dark lord is just WAITING for me to give him a full-on cannon burst to the chest. You just can't wait for that!
Here's a thought... If you want to have an option for your Inn that takes advantage of people sleeping, give them something to do for a bit... like a bonus for reading a journal or monster log. Your characters are sleeping peacefully while you go do all that tedius maintenance like organize your items, study up on the last boss.
My second thought while going over that last paragraph is... I would rather just hit the sleep button, hear a cute little twinkly lulluby, and wake up fully restored. STILL... I'm sure you could come up with some sort of bonus for waiting and reading, etc.