Haven't done that yet, but I can tell you that these adaptors *only* work as Printer Port, no Modem, no Scanner and no Faxmachines. So they most likely won't work for F2A, too. There is a native F2A USB version available for ~20 USD at a a lot of shops, though.
If the cart is a Flash2Advance then the cart itself isn't neither parallel nor USB
Probably you mean a parallel linker, or a kit made by a parallel linker plus a cart.
The name of the parallel linker should be a FlashAdvance Linker, without "2".
I cannot reply to your question about the parallel to USB PC adapter.
But I think I'm not OT with the following infos about compatibility between old and newer F2A/FA carts and linkers.
According to my experience you definitively can flash it either with the F2A USB Linker (the cable only) OR with the battery operated parallel thing;
Years ago I bought a USB F2A linker + 2 128 F2A carts; later I bought 2 second hand old carts (should be PRO, I'm not sure) with the parallel adapter, and I sold something mixing the stuff; now I can happily flash both the old cart and the new one with the USB linker; Both work perfectly with the Game Wallet, too. And the old cart is way faster than the new one, doesn't matter if using the USB cable or the game wallet.
The guy I sold the other things is happy using a new cart with the old parallel adapter
Also take in mind that a new USB Linker that doesn't require the GBA port has been marketd recently (can be useful if you want to play GBA game on a Nintendo DS ) You can consider it as an alternative to the cable suggested by enarky
have a look on www.gameboy-advance.net, maybe you find more infos