With the airgroup Eagle has plus the SHAR 1s and RAF GR1s and GR3s operating from Hermes (is it Hermes ITTL?) and probably soon to be operating from a hardened airstrip (Pebble Island?) - it's probably enough
I imagine that Eagle might possibly once the Bridgehead is established and supplies are ashore might possibly be able to head North for several days and take on replacement aircraft for her airgroup from Ascension - F4M is listed as having a ferry range of 1,750 miles / 2,816 kms / 1,521 NMs
Ascension to Port Stanley is a Great Circle distance of 3,889 miles (or 3379.5 NMs or 6,259 kilometers) - so Eagle would have to eat up quite a few sea miles leaving the task force exposed in order to take on replacements
Lets say she cruised at a relatively economical 20 knots - she could maintain 480 NMs a day she is going to be out of position for more than a week there and back (including I imagine at least one full RAS)
Also of the remaining F4Ks (18 in total of the original 28 RN ac in 1978) not on Eagle or lost for whatever reason - how many would be hanger Queens in 1982 (or 1978 for that matter) - I would imagine that many would be rapidly be made air worthy again (probably involving cannibalism of the surviving airframes of the 20 RAF F4Ks) during the period that Eagle was travelling and conducting ops down south
So it's not impossible - just pointing out the basic logistics of it.
Unless um by possible chance say the USS Nimitz or one of her sisters just happens to be innocently conducting cross deck exercises in the Central Atlantic - just saying like....