Surprisingly, the answer seems to be a qualified yes, however the texture is not the same. The dried gnocchi turned out to be much better if fried after boiling; see below.
Here are the results of my experiment:
I dried a small amount of the fresh Gnocchi by placing them in a 150 degree (Farenheit) oven for about an hour, then turning off the oven and leaving them in all day. It is very dry here, so that did the trick.
I boiled the dried gnocchi after several days of storage. They took about ten times longer to boil than their fresh counterparts. Even after they were fully cooked, they were not as soft as the fresh gnocchi, and they never regained their original size or shape. Overall, they were denser, firmer, and less sticky. Not desirable traits necessarily, but they were quite edible.
I decided to pan-fry a small batch in about a tablespoon of oil, and these turned out wonderfully! I have pan-fried gnocchi before, and it tends to be hard to keep them intact and keep them from sticking. The previously dried gnocchi, however, did not stick and held up to vigorous frying. The result were gnocchi with a crispy exterior and soft (if somewhat dense) interior. The crispy outside and flavor reminded me of samosas. These weren't just edible, they were great. I plan to dry about half of my next batch and use the dried gnocchi exclusively for frying.
It may already be an implicit assumption, but I think that time to cook is probably not as important as how to cook. While the power setting does affect the time to cook, the importance of time is to control how hot the parts of the food get.
As with all cooking, there is a need to control temperature. Running the microwave at less than full power allows time for the heat to be conducted from the hot parts to the cool parts. It is similar to searing vs. sauteeing.
I think that the accuracy of most microwave oven's power settings are good enough (my own testing shows about 10%). I would be more concerned about how I wanted the item cooked. Some examples:
- When I want to reheat things like a thick soup, I run the microwave at full power for a short period of time, stir, and run the microwave again. Stirring the concoction distributes the heat faster than the conduction process.
- When I want to defrost frozen foods (think meat), I use the lowest power setting. This prevents the edges of the food from getting cooked.
Best Answer
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.