First of all, you don't apply for Seabees as an officer. You apply to the Civil Engineer Corps which is the officer community that has Seabee billets. Roughly 15-20% of the billets are seabees, so you probably won't get one until your 2nd, maybe even 3rd tour.
Finally, to answer your question, I don't think the ASTB is required for CEC (correct me if I'm wrong, somebody).
If you want more info, check here:
http://www.cec.navy.mil
*UPDATE*
Starting in 2007, the CEC is now detailing officers to the Seabees within their first two tours, so if you don't get one right out the gate, rest assured, that's where you'll go next. In other words, ALL new CEC Officers will do a Seabee tour before their 4-year commitment is up.