Today for lunch at the office I have a package of gnocchi and a jar of tomato sauce. We have a microwave and a water cooler/heater. Is it possible for me to actually cook this up?
Put the gnocci in the tomato sauce with a little extra water to compensate for the absorption from the gnocci, and then microwave until done to your liking. You may need to add water as it cooks, if they are very absorbent.
The cooking time is likely to be longer, maybe even a lot longer, than boiling. You will also want to stir every couple of minutes for even cooking.
I have done this with traditional pasta when my gas was out, and it works well. As gnocci are essentially another type of pasta, the same technique should work.
I'm going to propose a different cooking method that's closer to cooking it on the stovetop; gnocchi when cooked wrong can be quite dense. It's still edible, but it's not as enjoyable.
** as you said you had a combination water cooler/heater, you can start with hot water, and skip steps 2 through 4.
I would use the water heater (or an electric tea kettle if there is one) for the gnocchi for a couple of minutes, then nuke the "cooked" gnocchis and the sauce together for 1-2 more minutes.
(this is because the gnocchis need to fluff-up and expand in water, just using a microwave with water wouldn´t produce that because it would cook them from the inside out and result in a denser structure...though they would be still eatable and taste more or less ok)