Stickies won't stick to these brush entities (at least, there's probably more):
func_brush
func_lod
func_clip_vphysics
So basically what you do is set up a brush entity that covers the door that the stickies will bounce off. Then when the round starts, kill the brush so that players can run through it.
func_clip_vphysics is unique in that stickies bounce off it, but it's not solid to players.