I had an older 32gb card that was originally in my Vita, and had a lot of games on it (I now use a 64gb card in the Vita, saved the 32gb card for the PSTV). When I put the 32 into my PSTV, it recognized all the games already on the card (but didn't carry over the folders). So all the games were there, but some of them don't work on the PSTV, they give an error when starting up (not supported).
On a side note, I'm assuming you have a separate Vita memory card for your PSTV? If not, you really need one. The PSTV internal memory is only 1gb, not enough to hold much at all. Just get a new memory card to be dedicated to the PSTV, use Content Manager to backup your existing games to a PC, and restore those games to the new memory card, then put the new card into the PSTV.