I was browsing the online application form the night before my LTC class was scheduled. I looked around and saw no reason why I could not go ahead and start the process, so I did. At the class the next day the instructor was giving some info about applying online and I specifically asked him if it was ok that I already did this and he said no problem.
I already scheduled the fingerprinting and it was to be done the following Tuesday.
Here I am 10 days out (from taking the class) and all docs have been received and status is now pending background check.
So I say, yeah go ahead and start the process even if you have not taken the class (provided you will be taking the class in the near future). This way the ball gets rolling and just awaits the proper forms (fingerprints, CHL-100, etc).