Yes and no.
Yes, It should in a context where not is a real Boolean operator. In that situation, it’s equivalent to tag is not gap. Note, though, that you’re using parenthesis here – that makes not negate the whole expression. Without the parenthesis, it would (perhaps) negate tags, like in (not tags) is gap. „Perhaps“, because tags might not be a Boolean expression and thus can’t be negated.
Like in the context of DT.
Which brings me to the „No" part. DT does not follow the model of Boolean logic with its search operators: They are not applied to expressions but to search terms.
text: me AND you
is valid DT syntax
text: me AND tags: you
is not. and is implied between all search expressions. You’d have to use any: to have DT or expressions together. And there’s no equivalent for not to combine expressions – you have to use a negative operator for that.
text: me tags:! you works
text:me not(tags: you) doesn’t
Personally, I’d like a more „logical“ logic in that context (which would reduce the number of operators, too). But most people are probably happier with what DT does now.
Which is, btw, very similar to what lots of apps do. Implementing an interface for arbitrary logical expressions is hard if not impossible.