I have done this several times - once on purpose, and two unintentonally  - I had issues with dew in the morning every time. Not a big deal if you have a covering on - but remember even "cowboy camping" is traditionally done with a canvas tarp cover - this gets the dew. - and a blanket underneath
My problem with doing this is most of the areas I go to are subject to unpredictable and extreme weather changes - so I can go to bed with clear skies and have a thunderstorm in the middle of the night.
Often if I don't suspect bad weather, what I do these days is to set up my hammock, hang my tarp, and throw one side over the back - so I am essentially open on the front. if I wake up with the weather changing I can then trivially stake down the open side in about 15 seconds and I'm good - this lets me lie out and fall asleep watching the stars, and still be able to not have a complete middle of night goonshow if the weather turns.
 - once on purpose on a horse trip - with blanket and canvas bag.. two times unintentionally on "stress relief" backpacking trips with a nice dose of single malt, warm fire and pad next to it, and falling asleep outside without getting into my shelter!