Yeppers.
Here's my "version" of how to patch the game. It may be easier to understand...
First things first, get a clean ROM of Pokemon Fire Red. Also, you'll need the Pokemon Shiny Gold IPS patch. We've got the IPS file on GBAtemp, so download it
here!
Now you'll need to patch the IPS file to the Pokemon Fire Red ROM. You'll need software in order to do that. I suggest using the free, easy-to-use Lunar IPS (Download
here). Once you've patched the ROM, you need to patch that same ROM to be compatible with your Slot-2 flashcart (unless you're using an emulator on your computer, they play straight up .GBA files).
Patch the Pokemon Fired Red ROM with the Pokemon Shiny Gold IPS file and you're good to go!
Simple simple simple.