You can double a track, but if you do, you should offset it a little bit to avoid the phasing Herb talked about.
If you never offset it, it remains exactly in phase and the only difference is that the track now sounds louder. You get no stereo spread and you get no doubling or thickening with an exact copy in phase. If you want to have some fun.... do this, copy a track, and then find the "swap track phase" button and swap the track phase 180 degrees. Solo both tracks so they are the only ones playing and hit the playback button. You should hear silence since both should be canceling each other out. Now... raise the volume fader on one. See what happens. Return it to the exact same level. Now add reverb to one. Hit play. You should only hear the reverbed signal. One more test to do.... With both back in phase and no reverb.... move one of the tracks about 1ms from the other. Play them and listen to the phase interaction carefully. Now move that same track another millisecond and repeat. Move it again.... now, add a third track and put it in the middle between them in a timing manner, listen again. You will start to hear some very interesting things going on. Mostly things you do not want happening in your mix. This will teach you a lot about phase and how it affects the other exact signal and why you need to be aware constantly, of the issues that can arise from phase problems.
Actually, when you offset it, that's when you run into trouble. If you offset so far that phasing isn't an issue, you end up with a distinct echo which is often NOT what one is looking for. So the track is often moved just a few ticks on the time line. Essentially a few milliseconds. Now, you have opened the door to the phasing and comb-filtering issues to join the party. Since you are now "mixing" these two tracks together in your rig, you now have the algebraic equation happening that is changing millisecond by millisecond depending on which particular frequency is mixing at a given point. It is practically impossible to avoid entirely when copying tracks and offsetting them. Reverb also plays a part because it is extending the frequencies by a certain amount. It is lesser of the causes. The interaction of the tracks is the big issue.
This is why, the majority of engineers would prefer to have a clean recording of a vocal several times to do the doubling as opposed to a copy/paste which is faster and requires less time on the singers part. No matter how close a singer sings the track, it will never be an exact duplicate. There is still a danger of phasing and comb filtering issues to occur, so using this method isn't foolproof, but the issues are to a lesser degree and easier to deal with due to the imperfections between the several tracks. Using this method, one does not have to offset the tracks. The imperfections in pitch and timing, while very small with a good singer, will provide enough variation to allow the thickening and doubling the engineer is seeking. By keeping those secondary tracks well below the original or main lead vocal track by -10dB or more (engineer's call), and panning it to the left or right of center, (remember that the algebraic thing happens when 2 signals are mixed together. panning mitigates that to some degree) the minimal phasing is essentially buried in the mix and is for all intents and purposes, a non-issue in the final mix.
When I use thickening, I use 3 tracks. One panned 100% R, one 100% left, both of which are at least -10dB below the lead, and one centered and much louder. I have used a single vocal take and copied it for this purpose. And it's acceptable to do that when there's absolutely no chance that you can ever get another take from that singer. Then, you just have to do what you have to do.....although, if the results end up filled with issues and artifacts, the best option is to delete the offending copy tracks and simply go for a very nice clean, well eq'd and reverbed solo vocal track. It's not impossible to get.