Yes VA have a mobile boarding pass option. I am however unsure if they will issue one without a passport check ex-LAX. There are no kiosks at their LAX check-in. I'm guessing that you have to see an agent no matter what.

Oh, and VA like a few other foriegn airline has very strict carry-on rules. 7 kg carry-on limit, even for J. They do give some concessions for laptops, an extra 3kg I think. But although I travel light, and rarely check in the USA, I would struggle to cross the pacific with only 10kg luggage. So most people check bags.