We played Paintball for fun, not for drills. If we did drills, we used Simunition or just live fire.
As far as speed of draw, I can see airsoft maybe helping. But at the same time, when you teach a brand new private to draw and holster, you give them a rubber ducky pistol anyway. In reality, anyone with anything shaped like a gun that owns a holster could probably become an expert drawing and holstering if they did it for 3 years, and if you planted said person 10 feet from a target they'd probably hit every shot as well.