Of course it's possible, why wouldn't it be? After all, once you defeat them and all the Stadiums you face your Rival who has Lugia, Ho-Oh and Mewtwo. On defeating him you have access to Round 2 Mode, whereby you can fight the Gym leaders, Elite Four, Stadiums and your Rival again...except on a harder difficulty. If you're struggling now, you're in for a world of hurt later.
Question answered, thread closed.
~Psychic