Yes, you will be an employee the first day and will be able to list. They will give you the number the first day and from there it is pretty self explanatory. Listing early does not give you a better chance of getting on, it is all based on seniority and what company you are a part of and what company the plane is.

I haven't had much luck with my ALPA mentor, only heard from him once. I've found this board to be a much better resource for information as well as asking other people around the center how things work. Plus you won't get your mentor till the end of training.