No. The only way a sleeping Pokemon can use Uproar is via Sleep Talk, and Uproar is one of the moves that Sleep Talk cannot select.
>Assist
Bide
Bounce
Chatter
Copycat
Dig
Dive
Fly
Focus Punch
Me First
Metronome
Mirror Move
Shadow Force
Sketch
Skull Bash
Sky Attack
SolarBeam
Razor Wind
Uproar
Sleep Talk
