You get the benefits (unlocked ship components, structures, passive bonuses) but cannot continue researching along that tech line like the civ the tech "belongs" to. You have to wait until they research the next tech, and buy that, too.
If I'm playing the Thalans, I can buy Manufacturing Centers from the Terrans. I get the Manufacturing Centers and the starbase module associated with that tech. I do NOT get to research Industrial Sectors on my own.