Unless an aircraft is specifically designed for aerobatics, it is likely that the wings will fall off at sustained negative g.
Or (my bold)....
Sec. 23.337
Limit maneuvering load factors.
(a) The positive limit maneuvering load factor
n may not be less than--
(1) 2.1+
for normal category airplanes, except that
n need not be more than 3.8 nor may it be less than 2.5;
(2) 4.4 for utility category airplanes; or
(3) 6.0 for acrobatic category airplanes.
(b) The negative limit maneuvering load factor may not be less than--
(1) 0.4 times the positive load factor for the normal and utility categories; or
(2) 0.5 times the positive load factor for the acrobatic category.
(c) Maneuvering load factors lower than those specified in this section may be used if the airplane has design features that make it impossible to exceed these values in flight.
As long as an airfoil is producing lift, there will have to be either some AoA, or an effective unsymmetrical airfoil. A variation on this will be wings with very effective flaps. Though the whole wing will still have a positive AoA to create lift, with the extension of flaps, the non flapped section of the wing might have a slight negative AoA, and no longer be producing lift. This is why some STOL planes have ailerons which droop with extension of flaps.
Aside from an AoA indicator calibrated to an airplane with effective flaps as described above, I cannot otherwise think of a reason for having an AoA indicator which read into the negative. I don't imagine that aerobatic pilots are considering the AoA indication during inverted flight.