Can you drain a RC helicopter lipo battery completely?

You can not drain your li-po battery completely. The general rule is to not charge them 100% completely, and not drain them below it's voltage. Doing so will cause the battery to begin puffing up and possibly blow up. Each RC helicopter has a manual and an approximate run time. The approximate run time is about 10-15 minutes. You should run only 10 minutes, which is the average run time on any aircraft.
References :
RC Pilot/Tech

I'll take all the typing out and agree with cycling magician.
References :
Electric / glow RC pilot and builder.

You do not want to over discharge lipo batteries! , No LIPO should ever be discharged to below 3V/cell UNDER LOAD, thats the advice from those who make em.

drain the battery below safe levels and cause unreparable damage to the battery and will never take a charge again.

If you plan on not using them for a month or more store them at half charge.

if ever the battery was ever revived, and it's not swelling, it's not defective, although it may have lost some capacity and/or discharge capability. But be careful with these things and use common sense.

the manufacturer of your Heli indicate the flight duration on the box. and some has abit of allowance that if your heli still running but fail to fly it means time for a recharge. even my walkera heli has a safety cut off feature that takes control of the heli's throttel and lands it w/o me controlling it to do so.
References :
http://www.trextuning.com/forums/showthread.php?t=6673

http://forums.radiocontrolzone.com/showthread.php?t=229585