ITA Airways from SFO to FCO

Hi everyone,

I'm trying to get from LAX to FCO in a couple of days and it seems my best option is ITA out of SFO as the flight is pretty wide open. Every other flight out of a US airport to FCO that day is a bit too tight with seat availability on my day of travel.

My questions are, will I get a seat assigned via the app when I check-in? Since I'm repositioning from LAX to SFO, I'd like to stay airside. I've also read on previous ITA posts that they are strict with carry-ons while checking in, another reason I'd like to stay airside so I can just go to the gate and keep my bag in case I don't get on.

Thank for any assistance or advice anyone can provide :)