Well, I was in your case, really enjoyed my curly hair but cut it for the phase 4. Don't know if it would have changed anything but it's better not to take the risk.
Then you'll see, once in NZ, that instructors are young and simply do not care about your hair style (within reason).
My hair are now quite long and I haven't had any trouble so far.
Don't take any risk, have a nice hair, it's well worth it.
Good luck for your sim.