If this were a manned launch, I would guess that unless the telemetry showed something very off, they would most likely have completed the full second stage burn. That would have left Dragon in a 190 x 205 km orbit, which is stable. If I understand correctly, SpaceX doesn't do orbit raising for Dragon by restarting the second stage engine (which is where the RUD happened on this Starlink launch), but rather uses Dragon's own thrusters to raise orbit. So most likely this would have been a successful flight.

On Starlink flights they don't have the margin to reach a full circular orbit on a single burn. It's more efficient to achieve an eliptical orbit initially, then coast and perform a second burn at apogee. It's that second burn that proved problematic this time.

Edit: having watched the videos, it would have been clear to SpaceX that they had an oxygen leak right from the start of the second stage burn. So I guess it depends on whether the pressures and flow rates within the engine looked OK. If the leak was external to the engine, then the main risk would be running of out LoX - engines really really don't like ingesting a gas bubble instead of liquid. If it looked like they were getting low on LoX, I'm sure they would have initiated one of the abort modes. Otherwise it's probably safer to continue to orbit. They do have cameras inside the tanks, in addition to all the telemetry - they have occasionally shown then on the livestream.