Like Pat said; if the tracks are simply flat or sharp across the board, then yes a pass thru the Pitch Shifter will indeed move them up/down slight amounts with virtually no noticeable issues.

Are the "music tracks in A" you are trying to adjust to MIDI tracks, audio tracks, or a combination?
If MIDI there may be a better way that can also do a tiny bit of 'auto tune' in the same pass, depending on plugins available. This would eliminate the guesswork of how many cents to adjust them.
Otherwise, tinker away with the pitch shift .. you may even be able to find a plugin to tell you how far the vocals are off in one pass, so you know where to start with the Pitch Shifter function. Again, reducing some of the guesswork.

Pat mentioned using the 'Undo' between efforts, I'd also recommend making a copy of the song in the first place to work on.
Like most engineers will say; use belts AND suspenders if you want to be sure your pants never have a wardrobe malfunction <grin>

I do not work here, but the benefits are still awesome
Make your sound your own!