Yes it is possible, but a lot harder then normal and the dream u will get won't be so rewarding cause it won't last as long and the quality won't be that good at the same time.

I never got to a dream yet, just sp (vibrations and so on) and some hallucinations. or i just fall asleep without knowing. But i think in dream yoga it's one of the goals to stay conscious for atleast a entire sleep cycle, without prior sleep that is.

Anyway good luck