The MB339s put in an attack Argonaut on 21 May. Pilot was awarded the Argentine equivalent of the CGC. Caused slight damage, including putting a hole through the radar (which is reported to have worked much better than before afterwards...)
AIUI, the strip at Stanley wasn't long enough to allow them to operate with their preferred anti-shipping weapon (500lb bombs) so they had to use 30mm cannon (podded) and Zunis, but they certainly flew. They were used at Goose Green, one being downed by a Blowpipe - apparently something that had an adverse effect on Argentine morale at the time. They withdrew about a week before the war.
In the grand scheme of things (and as I've said elsewhere, this was a scheme about which Admirals Lewin, Leach, Fieldhouse and Woodward were far more enthusiastic than the then-CAS), the ability of CAS aircraft to operate from Stanley was not the point. The point was to try to keep the Argentines' air superiority aircraft on the defensive/drive them out of range while making the junta worry about whether or not the British PM, who they'd realised was just slightly more bellicose than they'd thought would then turn the bombers onto the mainland.
The fact that they failed to appreciate that this was hugely unlikely was neither here nor there - they seem to have perceived that there was a risk and the moral effect of which air power theorists (and Bernard Montgomery) talk about came into play. Just as the RN (not the RAF) had hoped.