Can I match new to existing polyurethane floor finish?
I hope I'm understanding your question correctly. You have varnish pulled off your floorboards from tape, right? 

You can apply a finish that will look reasonably decent. It isn't likely to be a perfect match. Try to match the sheen. Also try to match the formulation of the original varnish (oil/poly). I wouldn't sand the raw wood, but I would lightly scuff the adjacent varnish with 220 grit to give the edges something to grip. 

Sand very lightly between coats and use a tack cloth to pick up dust.

You might do a small test area to see if the color matches, and tint the varnish if needed.