Yes. Still many things that could cause it to stop reading correctly, but that is indeed a good first test.
If you ground out the sending unit wire up at the engine, and the needle pegs to full (or just beyond) then the circuit and wiring are good. At that point about the only thing it would normally be is the sending unit.
Just make sure you have a good engine ground, but if you are able to start the engine then that ground is sufficient. And certainly more than sufficient to work a little ole gauge.
Paul