The "dimples" are the least of your worries. Squeaks indicate movement of course and movement under a ceramic tile floor installation is fatalistic for the tile installation. It depends on where the movement is coming from.
If the movement is simply a lack of fasteners in the subfloor (to the joists) then yes by all means screw through the tile. If this stops the squeaks your in luck. The problem is: Why would you want to put the life of the ceramic tile installation in the hands of the adhesive holding the vinyl in place?

The industry recommends that all previous floor coverings be removed before attempting a new installation of ceramic tile.
