No, they do not have enough work to keep them busy.
I have heard from several legislators about this (Gretchen Guess, Max Gruenberg, and Andrew Halcro to name a few) and they all agree with this. It has been brought up time and again, but the legislature will never bring it to a vote.
The reasoning behind this is that the first month of the assembly now is just wasted time. Absolutely no work gets done. None. I say, cut back the time the are there so they get the work done and get out of there. Why pay them to sit around and waste time?
If an important issue arises out of cycle, a special session can be called to deal with the issue(s). This prevents the governor from running amok while the legislature is out.
Besides, if the legislative session needs to run longer, they can. The constitution allows them to meet for 120 days from the date it starts without any special action. It will not look good for them though if the people of Alaska have voted to keep their sessions at 90 days and they are always going over.
Here is the pertinent portion of the Alaska Constitution: http://ltgov.state.ak.us/constitution.php?section=2
I hope this answers your question.