I've been wondering if I use the GB Interceptor to capture my gameboy game (with the real cartridge) do I need to classify the run as an GB emu, since it emulate the game. Or is it not allowed

Looking into this, it seems the consensus is that its capturing the gameplay using the actual cartridge. I've never used one, but I would say as long as it doesn't modify gameplay at all that submitting it as a regular run would be fine. The leaderboard isnt split between emulator or original hardware, so will be fine.