Absolutely! I did the same thing. I have an unlocked 820 and am using it flawlessly on AT&T. As far as updates go, it depends what region your unlocked 820 came from. Mine is from the UK, so it gets updates very quickly directly from Nokia. If your device comes from a region, Asia, for example, it may get the updates later. Nokia pushes out updates to different regions at different timetables. I got my UK unlocked 820 updates long before AT&T pushed out updates for their branded 820. I say Go for it! You won't regret it. Plus you can travel with it.
As far as LTE goes, I don't think its possible unless it supports the correct LTE bands. Most unlocked phones support HSDP (what folks here in the US call "4G")bands, though. To be honest, I can't really notice much difference between 4G (HSDP) and LTE anyway. I'm in a n LTE market too (San Diego).