Yes,it happens but I find loads of foreplay and a sensitive sexual partner can eliminate the stress-related lack of release.
I always compare sex with a car journey through known or unknown territory with the same end destination. You can get there fast or slow or your car can break down on the way. Why worry when you can enjoy the scenery and company, whatever the situation?
Sometimes I do this on purpose when I play with my morning wood. It wakes me up without causing a mess, and I still have the energy so I won't just go back to sleep afterwards.
Actually, rolling over and going back to sleep is what I usually did as soon as I woke up. Then I'd sleep until the late afternoon. To break this habit I printed out a bunch of celebrity fakes and stuck them to the bedroom ceiling. The sight of them would catch me mid-roll and I'd start playing with myself until I was too awake to fall back to sleep.
The problem with this plan was that if I came, I'd go back to sleep anyway. Then my left eye stopped working with my right and I couldn't see the ceiling so well anymore. Turns out using my imagination instead was the better way since my brain doesn't shut down again as easily as my body!