I leave my iMac on all night for video encoding, and have rarely slept the machine since purchase. I even turned off the option to sleep my hard drives.
You will be fine. If the iMac can't stand being on constantly then that is grounds for a replacement or refund.
It's gonna use some power too. Are you really printing from mobile devices 24/7? Energy Saver pref pane has a setting to schedule waking and sleeping, and you could use something like Alarm Clock Pro to schedule with more detail.
Only thing that may be an issue is it might cut the life of the screen. Course that would have to continue for some time. But that would be the biggest thing.
You can just turn off the screen by pressing Shift-Ctrl-Eject (if it doesn't work then I messed up and you should google it). As the screen draws the major portion of the idle power, you can also save soem money this way.