I've found that after a hard workout at the gym I sleep better and longer. That's certainly not a life-threatening injury but working out to exhaustion does create micro-injuries to muscle tissues which then have to heal (leading to growth).
I vividly remember the difference intense hockey conditioning camps, sleep and recovery can cause. During these camp I pushed my heart, with many drills being 30+ seconds at max heart rate. Afterwards I was exhausted, chest felt terrible. But I was so tired, I didn’t have the usual movements at night, and had much longer deep sleep. The recovery the next day was so dramatic compared to prior workout sessions. Way less inflammation across my joints. As compared to sessions where I only pushed my heart rate to 30-60%
Yep, I usually average more deep sleep (10-15m) during times of regular workouts. I typically fall asleep much faster as well, though I don't typically have issues with that.