Google Play - Review process through Alpha, Beta and Production channels
Just wanted to give an updated answer, I just did an internal to alpha, waited about a day and a half under review. Did an alpha to production and now I'm back under review. Just wanted to post this because I found the correct response to be outdated. If you are like me and are fixing a critical bug, it may be better to skip any kind of a alpha and go straight to production for quicker rollout.
Well, tested it myself and I can confirm that once the review has been passed on any channel it is not needed anymore, so the promotion to production is right away (more or less, as it takes a while to propagate, but there is not new revision).
There is an important difference between Internal Testing and other tracks.
If you push the app to internal testing there is no review (at least not the long one as on other tracks) so pushing there is almost instant (except the first release, from my experience this one takes a bit more time).
Case 1.
Push to internal test -> no review. Push from internal test to alpha -> review.
Case 2.
Push to alpha -> review. Push from alpha to prod -> no review.