Hello I'm considering run. But I've got PAL PS2 already and don't want to mod it neither buy another (ntscj) one. Is it allowed to submit run playing game from HDD?

as long as it not mod the game, every platforms allow

I changed the Emulator board a small bit, it now allows Digital runs (as in loading the game from an HDD or SSD). Using optical Media is for the main board, but if you want to use Digital ways to play the game, you can submit it on the Emulator/Digital board!