EMB-145 Captain reported encountering wake turbulence just before touchdown from a preceding Airbus that resulted in an EGPWS 'Don't Sink' alert. Reporter stated the aircraft energy state was low so a decision to continue to a safe landing was made.

Narrative

Landing [Runway] 36R in CLT with flaps 45; Pilot Flying (PF) was a Line Check Airmen (LCA) in the right seat doing Captain upgrade OE. Upgrade Captain was Pilot Monitoring (PM). We were approximately 4 miles in trail of an Airbus (type unknown). The Airbus touched down approximately 1;200-1;500 feet down the runway; and turned off (I believe) on Runway 5/23. The aircraft was clearing the runway when we were approximately 500-600 ft. AGL. Winds were 040-050 at about 4-6 knots. Approach was smooth; stable and uneventful. Upon crossing the threshold around Vref to Vref+3; we encountered wake turbulence with at first some left/right wing rock; but nothing that isn't typically encountered for landing in CLT. The PF could feel the aircraft lose lift; and added substantial power. The engines were already stabilized from the final approach; at my best guess is 60-64% N1. PF added power nearly to the thrust detent and felt the airplane respond; with the induced sink rate arresting approximately a few feet from the runway. An EGPWS 'Don't Sink' aural message was presented. The PF did not hit TOGA; and with the airplane in a slow airspeed state barely off the runway; the PF believed the safest course of action was to idle the throttles and get the aircraft on the runway. A smooth landing was accomplished and the aircraft rolled out with no further incident.PF/LCA was surprised with regards to the Mode 3 alert that is normally presented for climb out situations where the aircraft begins a rate of descent. The environmental conditions were ideal for a potential wake turbulence encounter given the previous aircraft touchdown point; and the gentle quartering headwind on the field at that time. I would very much like to see the metrics from the event; as well as the EGPWS logic that was presented given the conditions. While a go-around was certainly a viable option at that time; given the energy state of the aircraft when it recovered and its close proximity to the runway I believe setting it on the ground was the safest course of action at the time.