To answer your question, we use to have vinyl tiles in the foyer. 2 layers of them. Vinyl on luaun, then vinly on luaun again. What a mess! I simply ripped up both layers, one at a time, right down to the original subfloor. I then installed a hardwood floor.
So, yes, to answer your question, you could save some $$$ and go right down to the subfloor. Just figure in your mind what the 'thickness' of what you're ripping up is compared to what's being installed, underlayment and all. This may have an impact on doors, molding, room transitions, and so on. What I mean is if the new floor ends up being 1/4" lower than the old one, then you may see paint lines along the wall. Or, if your new floor ends up being 1/4" HIGHER than the old one, you may not be able to open some doors. Certainly you'd save some $$$ on the labor to demolish the floor.
If you do your own demolition, I used a combination of a coal shovel and ice chopper to 'lift' up the old underlayment with the vinyl still glued to it. As I mentioned, I had to do the room twice since I had 2 layers. My best to ya and hope this helps.