I know when I do this that I install new plywood if there is any question about the condition of the existing surface. Most of the time we would lay 1/4" luan plywood over existing 3/4" plywood t&G underlayment (subfloor) in order to stagger all of the seams and flatten out imperfections etc. We always used mucho construction adhesive and either ring nailed or screwed it down. Usually, the vinyl subcontractor would use "levelastic" or other filler to flatten out seams and nail holes. You might want to ask them what they mean by "underlayment", ie: exactly what they are putting down - thickness - and also how they will treat the transitions between this and neighboring floor surfaces and levels. If they are going to add 1/2" plywood or sim. then how will this affect the edge where this floor meets your carpet or wood floor?