The angle of attack will remain in its usual very narrow range at any point when you fly a loop. The critical or stalling angle of attack is typically around 15° - 20° for many airfoils (so your AoA should be less than that). Note that if you fly upside down (negative-G capable aerobatics airplane) you will still have a positive AoA, just on the other side of the wing.
> If the airplane you’re flying is equipped with an angle-of-attack indicator, it will illustrate an abstract concept that pilots learn to recite during ground school but rarely fully comprehend—which is that an airplane can stall in “any attitude” and at “any airspeed.” For me, it took stalling on the back side of a loop (while pointed straight down at a high power setting) for that idea to sink in.
https://www.aopa.org/news-and-media/all-news/2013/may/pilot/...
I would use AoA in relation to the direction of flight, not the up or down orientation of the airplane. Even upside down I still fly quite normally (in straight & level upside-down flight), and the lift created is positive: Up/down in relation to the earth don't change, so the direction of lift does not change. In this context it would be a bit confusing to use negative numbers as you suggest, IMO.
However, since you can set your relative coordinate system and context however you like this is a topic we could discuss this ad infinitum without convincing one another if we insist on our respective PoVs. When faced with the linked question you would have some more explaining to do though, because there are negative AoA and no upside-down flight (now imagine adding that to the question to make it even more confusing...) :)
Edit: Oh you meant flying upside down, not doing a loop?
Yeah, negative AoA is not the same as positive AoA. It makes sense to distinguish them because, unless the wing uses a symmetric airfoil, it will behave differently in the two cases. Given that you also calculate the lift vector as a function of AoA, and for anything to make sense the lift vector is antiparallel in the two cases, the AoA would also be negative.