I am mixing a rock song, the lead vocals have been doubled during the choruses. I basically treat the doubled vocals same as the main lead vocal, except I compress them a bit harder.
question is: do I also apply reverb to the doubled track, or do I leave it dry?
I think it would depend on what sound you are going for. I usually send all of my vox to a Vocal buss and have whatever processing I may want (other than possible individual track compression and eq) I put on the buss. That way everything sounds like it is in the same space sonically. You may want to treat your background vox differently, but again it is just a matter of taste IMO.
Whatever sounds good is good. I even remember sending only doubled vocal into reverb. You can try some stereo tricks: if you have more than one doubled vocal try panning them L/R, or if you have only one apply short delay /between 10 and 20 ms/ and pan original doubled track and delay hard L/R. Sometimes you have to eq differently taking off more low-mids or highs, and looking for more aggressive overall effect. It's not unusual to squash doubled vocal with compressor really hard, or even distorting it with some plug-in or guitar amp. On metal core mixes I did some time ago it worked great.
But if it sounds ok like it is its probably ok.