I would say yes. However, I suggest first removing any carpet or other floor covering. Cut the plywood to fit as needed. I'd use 1/2" thick plywood and not OSB or such. Use a liberal amount of construction-grade adhesive applied to the floor with a notched trial or adhesive knife. Place the plywood in position. Then use 1" #8 flathead wood screws on 12" centers in all directions. Don't over-tighten screws so as not to strip them from the floor. You may find it easier to pre-drill pilot holds, and then drill the countersink for each of the screws. Don't expect the screws to pull down into the plywood. Drill a pilot hole and then drill the countersink.
