Jedster has it right.
You can very easily use a pole for self-arrest even if you're wearing the strap. Having *both* straps on complicates it slightly, but it still works in practice very well.
When you need to arrest, you hold one pole by the handle (hand still in strap) and bring it around to where you can grab it just above the basket with the other hand. You bring the tip of the pole next to your ribs or waist and drag the tip *hard* into the snow surface.
If you can visualize it, you'll have one arm out away from your body (the handle end) and the other wrapped around the pole at the basket. As soon as you start to dig the tip, the drag will turn you so that you're on your side with your butt and back below you. That helps stabilize you, turn your body so that you aren't leading with your head, and slow you down.
There are obviously conditions in which this will not stop a slide, but it actually does work very well. Next time you're out, find a moderately steep, moderately firm slope (with a safe runout below) and give it a try. You'll be surprised how well it can work.
The other thing that's critical in this is that you start to arrest *immediately* if you ever find yourself in this position. The less speed you have to scrub the better.
A steep, hard-snow slope with uncomfortable consequences to a slide is the about the only time I *do* wear a strap. This self-arrest method may not be perfect, but it's one helluva lot better than nothing. That's why I want at least one pole to stay with me if I do go for a slide.