No, the UK did use the carriers - wiki quotes -
HMS Hermes
As she was the RN's largest carrier, she was considered too valuable to risk close into the Falklands, due to the possibility of Argentinian AF attacks. Her Harriers therefore operated at the limit of their endurance radius, but were very successful in keeping the enemy aircraft at bay.
HMS Invincible
The Falklands War saw Invincible, and the larger and older HMS Hermes filled to capacity with both the Sea Harrier and the Royal Air Force Harrier GR3 ground attack variant of the aircraft, along with ASW helicopters. The RAF Harriers proved to be a temporary aberration at the time.
The RAF Harriers were a problem since their INS (Inertial Guidance System - pre-GPS) could not be easily initialized on a non-stationary vessel at sea.
If you are talking about the sole Argentina carrier "25 de Mayo", then you are correct in the fact it was not used, but I think it was more fear of it being sunk like the Agentina battleship "Belgrano", not a concern for the population.
Attacks were being prepared from the 25 de Mayo - from another reference -
Earlier in the week before the British arrival, ships of the Argentine Navy sailed from the north and south of the Falklands as Task Force 79. By early Sunday morning (the 2nd), carrier "25 de Mayo" to the north was preparing to launch a Skyhawk attack which was aborted because of light winds, and that same day both escorting type 42's were involved in separate incidents. "Hercules" readied but fails to fire a Sea Dart against an approaching No.801 Sea Harrier, and "Santisima Trinidad" lost her Lynx in a flying accident [a9]. By then, submarine "San Luis" may have carried out the first of a number of unsuccessful attacks before she returned to port around the end of the month. To the south, Sunday also saw one of the most controversial incidents of the war - the loss of cruiser "General Belgrano" and over 300 men.
http://www.naval-history.net/NAVAL1982FALKLANDS.htm page 24
If a part reason for the war was to distract the Argentina citizens from their local bad economy, losing two major navy ships would have the wrong effect.
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