Is it not a bad idea to do this? We may well be able to self-serve find the answer, instead of having to raise a query and wait for a reply.

At least make it "license holders only" or part of the annual support contract.

I must say I agree with ncrossland on this, I understand moderating forums can take time but so does maintaining documentation and doing support...
What prevents anyone to create an ac 1.0 unofficial forums ?

Forums are "grey matter in action". Documentation is "static" and there is only so much support queries you can handle (if your user base grows exponentially this will be even more true...). Let me take the example of Expression Engine, since you chose it as a CMS for the activecollab website, and got inspired by what EllisLab is doing : the forums play an important part of EE support !

It seems to me it would be a strategic mistake to close those forums.
You need at least to keep them open during the launching phase and then make them private but close them ? Not sure this will help...

I think renaming to "Technical Discussion" would be much better, along with a notice that this is user-to-user only, and how to obtain official support.