Paul,
Whether it gets air out of the pistons really depends on which alternate you use. For instance, if you use the alternate bleed where the line goes in to the piston (right hand picture, lowest alternate point, just below the legitimate bleed screw) it will get air out of the piston (or the vast majority of it, anyway).
In any case, I agree that it is always best to get your bleed screws replaced and in working order. In fact, I need to do that for exactly the bleed screw mentioned above on my left rear caliper. Some idiot at some point in the past put a bolt, sans head, in where that bleed screw should be. It's not a broken bleed screw since there's no central hole in the thing like a bleed screw has. On top of it all, some idiot (probably the same one) managed to snap off the head on the fitting that goes in that same spot that could be used as an alternate bleed point. Very frustrating!!