Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
Do you mean time machine off or the mac off? Also, did you run a TM backup while the file you want was on your computer?

If you did simply go into time machine, scroll to the correct backup and retrieve the file. If your mac was off than no, time machine will not run a backup (although if it’s off, how did the file get deleted?) and most certianly if Time Machine is off it does not run backups.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.