Most Certainly, once you have and can use Cut and Flash, you can do the Gym Leaders in any order you wish; however to get to Blaine, you will need to beat Koga and get HM 03 Surf. You WILL need to beat Surge in order to fight Giovanni in Viridian Gym.
You can use the walk through walls glitch to get to Giovanni/Blaine/etc. early. The only requirement regarding the order you fight the Gym Leaders, at least with the glitches I know of, is that you fight Misty before Erika.