RUN 582 UL WITHOUT PROP

I would not run the engine without a prop. When regular GA engine shops run newly overhauled engines, they do it with a short, fat propellor usually refered to as a "club."  I can't explain the mechanics for you, but maybe someone will come along shortly who can. Maybe it's ok with a ROTAX, but I wouldn't risk it.

Do not run the engine without a propeller.
The idle will be unstable without the flywheel effect of the prop. 
Without the air load or the momentum of the prop, you risk over reving the engine a split second after cracking the throttle off of idle.
It will rev up even faster than an unloaded motorcycle engine and overheat quickly without the cooling air flow.

Aircraft engine do not have or need the extra weight of a flywheel to smooth out the power pulses, the propeller serves that purpose.
Engine test stands will use a "Club" prop for the mass and load while minimizing the dangers of a full size prop.
The cooling airflow is often provided by separate electric blowers.

Be extra carefull,  Propellers can KILL!