Yes and no. During the majority of flight conditions, they are equivalent. However, during conditions where the aircraft is moving through a mass of air that has a vertical component, the behavior is slightly different.
As vertical updrafts are rarely of concern, the scenario to look at is the downdraft during final approach. In this environment, the aircraft will sink at a rate that is not consistent with the aircraft pitch. As the algorithm utilized compares the aircraft pitch to the actual flight path through the air, this will result in an artificial positive AoA (see diagram).
A downdraft that forces a sink rate of -1000 FPM will effectively increase the current AoA by approximately 5.6 degrees (this is speed dependent).
In effect, this makes the AoA thresholds more sensitive and an alert will be generated earlier than normal – but that’s a good thing in this scenario.
If a down-draft of this magnitude is experienced, the pilot action is to add power; Similarly, if AoA exceeds the configured limit, the pilot action is also to add power. As the pilot actions are identical for both scenarios, it can be argued that the source of unexpected altitude loss (downdraft or a wing losing lift) is irrelevant. Add power.
Interestingly, if taken to the extreme, the probeless AoA system actually starts to behave like a wind-shear alerter and any downdraft that is sufficient to cause excessive pitch vs flight path angle will generate an alert – it’s effectively a sink rate alert at that point.
In a probed system, as the probe is only measuring ambient air angle and loss of altitude is not measured, this arguably advantageous behavior is not available.