It might work, but not as you want it to. Which is to be expected.
In Boolean logic, the NOT operator negates the following predicate. In your case, the predicate would be tag is GAP. Consider the house is blue. Saying not the house is blue is very different from the house is not blue.
In the first case, you’re talking about everything that’s blue and not a house (“not the house is blue, my eyes are and my car is”).
In the second case, you’re talking about a house that has another color than blue.
No doubt. But in the documentation, “term” means “search term”, i.e. “GAP” in your context. Not “search expression” (like not tags: something). The same goes for AND and OR etc.
I find the usage of the word “term” a bit unfortunate here, as it has a very different meaning in mathematical and logical expressions. And that might lead to the false expectation that the boolean operators will work with expressions.
For the sake of clarity, using “search term” might be better in that place.