The flip side of that for me, as a long-term (25+ yr) insomniac, is exercise is the only thing that has ever gotten my sleep issues under control.

So, yeah, I think it's not smart to deprive yourself of sleep and still exercise. But if you're cursed with sleep issues, consider getting started on an exercise routine even with little sleep.

You may find out in a few weeks time that the sleep issues go away.