Yes, I don't believe the app has the capability to provide a boarding pass without a seat, but the kiosks and airport agents are able to. I'm not aware of any reason you'd need to show up to the airport early, just don't cut it close if you usually do. Typically they'll wait until just before boarding when they know how many people haven't checked in (and therefore won't be on the flight) and handle any roll ups. I've had it happen as late as after boarding has started, and it was processed when I scanned my boarding pass. The AA agent who was handling my flight last night (domestic) told someone they'd receive a seat assignment at 10 minutes before boarding (45 minutes before departure) and that's when I got pinged that I got upgraded (and presumably they got my seat).