Yes the refrigerant can act as a solvent, but the "damage" that it will do as a solvent is mostly visual, like discoloring plastics. You can spray it all over electronic PCBs and components and it is unlikely to cause a direct problem from solvent. Note: I am not recommending doing that at all, I just have at times and it did not cause any problems from that, but from moisture.
Things that can happen, you could cool something so much that an uneven contraction/expansion thing exists. Possibly hitting a really hot silicon component with it could crack it. Just like pouring hot water on a cold glass can break it. It must not happen very often because it has been used at times to force cool things. It would probably be unwise to have the machine operating when using it. There could be other things, that would suffer due to one side of them contracting a lot in the cold.
Another thing that will happen, and would be a very large concideration, the cooling of things will condence moisture out of the air. The water on things would be worse than the refrigerant after it started reacting as electricity flowed through it, particals are suspended in the water and all.
You would just want to make sure that not only the refrigerant is vaporised, but that any water condenced on the cold parts is dry again before powering it up.