It is possible to trade for specializations that you don't have in Beta 6. I have tested that...
But as OP found out... if you trade for one before you researched one you are stuck with the traded one, but you may trade for the others later.
I'm not sure if I like that you may trade for them, sort of remove the fun of that feature. I hope they restrict that and make the tech mutually exclusive even on the trading table.