The rule on extra mat time is different from dojo to dojo, but its generally allowed in some form or another.
Don't worry about the awkward things in the basic class. One of the best lessons that any martial art can teach you is to knuckle down, swallow your pride and throw yourself into learning something new.
I've been training under a teacher who learned Tenshinkai and have decided to expand my horizons at a nearby Fugakukai dojo. I feel like an idiot there. I'm the most senior student at the other dojo, but I can do about nothing correctly at the new one.
Don't worry about being a n00b. With hard work and dedication, you'll become l337.