Could draining my battery cause all of this?

Could draining the battery cause all of this?
My friend borrowed my 95 jetta, 160000 miles and left the lights on all night and drained the battery. When he gave me a jump, the car was shaking every few seconds and was revving up without me pushing the gas. now, when i drive it, it is idling strangely, it surges especially in lower gears, and it is constantly revving up, no matter what i'm doing with the gas.
i took it to my mechanic and he thinks it's the MAF. when he unplugged it, it would stop the revving. he wants to get it scanned before he has me order the $400 part! maybe something needs to be cleaned? maybe a new throttle switch? it was running fine before the battery drained. please help.

Well, the first step in any electrical diagnosis is to verify that you have the correct battery voltage.

If the car was fine before your buddy drained then battery then I'd start with a fresh, fully charged battery before I paid $400 for a part.

even if the battery is very new? (just got it a few weeks before this happened).

battery

Why don't you go to auto zone and have them test the battery? They will tell you if it has a bad cell or low charge. Yes you can do permanent damage to a regular battery by draining it down! A trolling motor battery for fishing can recover but not a car battery. What part costs $400. Not a MAF- go to impex or one of the many places on this site that sells tdi parts.