The error message when you try to extract DNA from a radded ship is something like 'can only extract dna from a non player owned ship'. The aveksaka AI are currently uncappable, so it's not possible for them to be player owned ships.

Steps to reproduce:
i. Rad an aveksaka
ii. Use the dna extraction beam on it

As a side note, it's really tricky trying to harvest dna as FC, it's one of those situations - along with hero 3000 - where I wish tractoring wasn't considered an attack by your slaves.
Your only real option is setting slaves to completely non-aggressive and RTS when you need to defend yourself, which frequently leads them to guard a location, hit the wrong ai, or if you have tradeslaves... guard the ai you want to attack