Not exactly:
The devil is in the details. Increasing pressure increases temperature.
If the gas temperature is increased, then you have a heat source that can be cooled. Releasing the pressure after cooling will cause more cooling since without pressure the helium would boil and evaporation is a cooling process.
Result: froozen!
Just put water in a closed container and create a vacuum. The water will boil without adding heat, but boiling / evaporation is a cooling process and the boiling water will change to ice.
It's like telling the boys they can't play with me; they get boiling mad and their attitude turns to ice. ( I don't have to give a referance do I ? )
