Maybe. People usually say if your intent is to solve it as fast as you can you are already a speedcuber. And since speedcubers speedcube, I guess that if you try to solve it as fast as you can you are speedcubing.
speedcubing means solve the Rubik's Cube as fast as you can with the desire of doing it faster every time, so it doesn't matter if you are at 10 minutes or 15 seconds of average to be a 'speedcuber'
In the extras for Pursuit of Happyness it is summed up.
"Being a speedcuber doesn't mean you have to solve in under 30 seconds, under 20 seconds. It depends on your intentions. If your best time was 2 minutes, and now you want to solve FASTER, then you are a speedcuber."
I might have gotten the numbers wrong, but the is it.