I agree, and so does science. Sleep deprivation will wreck your training efforts, make you weaker, more likely to store fat & break down muscle tissue while also making you hungrier.
http://www.strengtheory.com/sleep-pt-1/
http://www.strengtheory.com/poor-recovery-and-increased-musc...
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.
Reminds me of this attempt[0] I recently ran across to identify the central nodes of a habit network. A neat idea, and one I hadn't seen before, despite a pretty good familiarity with the literature of habit formation.
[0] https://medium.com/forte-labs/mapping-the-habit-graph-13e851...