Yes, you can.
In fact, you can even completely skip Brawly and proceed to beat the other leaders. This goes for Winona too, however you must return to them after finishing the other leaders in order to proceed to the Elite League. In order to fight Norman, however, you must defeat Brawly.
You don't really need the TM Flash in order to meet Steven. TM Flash just eases your way. It might be a little hard to navigate around, however, so it is always recommended to take Brawly down first.
Hope this Helps!
Source (Skipping Brawly)