Is it feasible to cover low-pile carpet with a 1/4" subfloor and vinyl tile in a kitchen?
I think you will regret leaving old carpet on the floor and covering it up. If you are willing to spend $$$ on plywood, why not spend those same $$$ on some foam underlayment for a solid vinyl locking plank floor? The foam is a decent sound deadener, water-proof and resists mold and mildew.

Old carpeting, even a low nap commercial type will hold moisture, breed mold and odors. One bad spill, pet accident, etc will become a smelly problem.

Rip it out and do it right, you won't regret it.