So I moved into a new home and the previous owner had the floors refinished with what looks like oil based varnish.

I wanted to add more protection so I cleaned the floors and applied water based polyurethane.

I've done more research and see that if I didn't abrade the surface the new coat won't adhere properly and it will peel. But it looks fine after 1 week.

Is peeling a sure thing? My dad says that if it isn't peeling after 1 week then it will be fine. Any ideas?

Time will tell.

Pick an out of the way place on the floor, and put a piece of duct tape down. Peel it up. If it brings the finish with it, then you'll know it didn't really 'take.'