Is the floor just a single layer of plywood, or is the plywood a second layer of flooring? Older homes around here sometimes had 3/4" ship lap or 2 x 6's layed down as the sub-flooring, then plywood or particle board underlayment was nailed down on top of that. In that case, if the plywood is of good quality, the vinyl flooring could be installed on the plywood after prepping it.
If your plywood is a single layer over the joists you will need the addition of an underlayment.