Can it be used as a bathroom vanity backsplash by itself? My vanity top has an upward lip on the backside that meets the wall, makes typical 1 hard?

Yes, you could use the bullnose "upside down" as a "starter row" if desired, then proceed with the tile. There would be no issue using the bullnose this way. A cleaner look might be to pull the vanity and sink out from the wall, tile the full length properly behind the vanity, then push the vanity back into place so it is now over top of the tile, and seal along that ledge. But if this is not possible, the bullnose method may be your easiest solution.