Ridiculous. You have to do 2 tiers of research on the Vasari tech tree and 3 tiers of research on the TEC tree in order to build either of those units. How are you going to pull that off as Advent? Now, if you captured an Advent builder, and you've done the research as Advent - sure, you should be able to use it. So go do a test and make sure that you can (post results here). Otherwise....
I meant, that when I (Advent) capture a TEC starbase constructor or a Vasari migrator (which as allready attained the starbase construction ability because the previous owner has researched it) it would be nice if I could buil those starbases. I have no idea if the current tier-game-mechanics would support that. It's just a thought/wish ; - D
With the Vasari migrator I tested this: the AI had definitely researched starbases and I as well. But the ability wasn't there when I converted a migrator 
In Starcraft capturing an enemy builder unit gave you access the enemy structure/tech tree, right? In some of the Command&Conquer games as well 
What I think ridiculous is the fact that converted ordinary frigates retain all kinds of stuff that you don't want as the new owner (movement orders, activated abilities, fleet assignements etc.) but such a cool and funny thing like converting an enemy starbase constructor is no use at all 
In this particular case I understand that probably the developers don't want Advent to have such an unfair advantage, that's OK. But then why are the other annoying things concerning converted frigates still happening?