Unfortunately, in order to do this properly you need to convert the .gme to .mcr using memcardrex which works fine, but then you need to use CWCheat for PS1 games which doesn't work properly when importing memory cards on Adrenaline. Basically what it does is import saves to a temporary memory card, which then gets saved to a slot 2 memory card. If the game features multiple memory card loading (like FF games), it'll show up in slot 2 and you can load/save just fine so it'll work for those games. If the game doesn't, you won't be able to access the save so you can't save it properly. This is likely because of the way PSP/PS1 emulation works on the Vita.
So tl;dr, if the game allows you to load saves from slot 2, it'll work ok. If not, you're stuck.
The only workaround that I know of is to use an actual PSP with CWCheat to load the memory card and save it, or ask someone who has a PSP to do it for slot 1 games.