A friend processed a vocal track for me but accidentally exported it as a stereo track. If I import the track with "as mono" checked, and just use one of the two resulting identical tracks, will the sound quality/track information be the same as if he exported it as mono? Or should I have him re-export it?

I do notice that the levels of the split mono-ified track are lower.

It would depend on what "processed" means as there may be more than dual mono channels going. You can also import the stereo track and bounce that track into a mono track, which will combine the elements of both channels.

The processing was fixing a few notes that were off pitch.
 
I just imported the stereo track, converted it to mono. Levels seem right now. So would this indeed be the same as if he just exported as mono?

Try it in your mix, and see if you can get it to sit right, that's really the bottom line (getting it to work in the mix).
My 1 st choice though, if it is available, would be to just have him re-export it properly.