no.. vinyl has to come up in order for the tile adhesive to bond. and some vinyl is also soft ,so your tiles will break or the grout will crack.
plus check how stiff the floor is by bouncing up and down and see the floor movement.(glass of water is a good guage). if it moves too much then you will need to glue and screw half inch plywood on top (can go on the vinyl sometimes if it is not soft vinyl) so the grout will not crack.screw to the joists and about 8 inches apart in a grid and use good constuction adhesive.