Yes, the airy draw is completely normal.
I've had one last 1 day (gurgling and leaking out of the bag, and after cleanings / etc. never got any better), and then a couple others I have 2 weeks on so far after a couple cleanings.
FWIW, I like the 'mini' T3 a bit better - noticeably reduced capacity, but better flavor (IMO) and less gurgling. On the full sized T3, that looong center pipe with the head pipe inside it just becomes a perfect condensation chamber. And liquid then gets trapped in between the two pipes - no amount of blowing will help because it's between the pipes, not the central tube.