Indeed. But the system already knows what the mass is, this is needed to calculate takeoff performance, rotation speed, stall speed, maneuvering speed, etc.
CG doesn't enter into it except to second order due to horizontal stabilizer lift.
It's still not enough information to compute AOA. Let's say I'm configured for 300kts in level flight. Now I pull back on power changing nothing else. I'll end up in a decent, and eventually that will stabilize to e.g. 1000fpm at 300kts. I'm still at 1.0g, and 300kts, but I'm in a decent, obviously angle of attack is less than in level flight. So airspeed and load factor aren't enough, nor is including mass.
Horizontal stabilizer lift is a downward force and must be countered with lift from the wing to maintain level flight. It's effectively the same as adding weight. Angle of attack absolutely changes as CG changes. This is a central purpose of weight and balance computation. W&B also changes as fuel is consumed. So you'd have to take that into account.
Anyway, you can't infer angle of attack or the coefficient of lift from only airspeed, load factor, and mass. You need more information.
I'm still at 1.0g, and 300kts, but I'm in a decent, obviously angle of attack is less than in level flight.
This is a common misconception, but is not true. The angle of attack does not care if you are in level flight, climbing, or descending. As long as you are in unaccelerated flight, the AoA is identical.
It's not exactly the same, because if the descent (or climb) angle is significant, the lift only has to supply part of the weight of the airplane (the rest being supplied by drag or thrust), so the AoA will be slightly less. But that's accounted for because the load factor will also be slightly <1G.
(The edge case is if the plane is flying straight up or down. In that situation, the wings provide no lift at all and the AoA will be zero.)
Replying specifically about the stabilizer lift discussion:
What you're saying is true, but the effect of AoA is not huge. Stabilizer lift is a small fraction of main wing lift, because it has a huge leverage. The corresponding effect on aoa (effectively stall speed) is noticeable but also not huge. CG matters mostly because of its effect on controllability, not because of its effect on stall speed (although the effect is there.)
I maintain that, for the purpose of judging whether an alpha vane has failed or you're actually about to stall, you can ignore this effect when estimating AoA.
It's exactly the same as making the statement "If I'm flying at 1.5 Vs0, I know I'm not stalling (unless I'm in a very steeply banked turn or is pulling up sharply out of a dive.)
I saw you're a CFII. If a student made the above statement, would you berate him for failing to consider CG position?
CG doesn't enter into it except to second order due to horizontal stabilizer lift.