Personally, I only butted heads with error 2002/5006 2-3 times tops before it let me in. Not sure if switching to the other data centers and back really helped, but...
Then my actual queue times for Sargatanas were never worse than 20-30 in line, so maybe a minute tops waiting there. After that, I never got disconnected or errored out. So I'm not sure that the entirety of the problem was at the front gate, and not partly to do with specifically over-crowded servers.
Overall though, my personal experience during the early access was far better than ARR's early access/launch, where I'd end up not being able to play at all for a day or more.