Yes.

Lots of posts on this, but the simplest solution IMO is to use your *G card at booking and check-in, then apply your UA # at the gate, kiosk, or online after check-in.

The UA kiosks make this really easy to do, if you'll be at an airport with them after security (LAX works great).

You can re-print your BP after doing this to ensure that your UA # is on your reservation. You may lose your boarding priority but not your seat (and you could probably show your *G card to board if you really wanted to).