Fog of war and all that. Low probability but still could happen.
The fog of war would have needed to have become very thick indeed. I would rate the probability as next to zero given the historical position.
Firstly the only aircraft the Argentinians had that was capable of carrying more than a single 1,000lb bomb from the mainland to the Falklands was the venerable Canberra. They only flew a very limited number of anti-shipping operations up to 1st May when one of their number was shot down. After that their main activity was night bombing land targets, mostly from higher altitudes with 1,000lb bombs.
As far as the Daggers were concerned their usual bomb load was 2 x 250kg ExAl bombs with either conventional (BR) or parachute retarded (BRP) tails. From 12th May the Daggers based at Rio Grande, but not their other bases, began to fly operations with the option of a single 1,000lb bomb of British origin. Looking through their operational history with that latter weapon at the missions that actually found a target to attack, they achieved the following:-
21st May - 3 aircraft attacked Argonaut & Broadsword no hits, one aircraft lost.
21st May - 3 aircraft attacked Antrim one hit failed to explode
21st May - 4 aircraft attacked Ardent & Brilliant. 2 hits on Ardent that failed to explode. 1 aircraft lost
24th May - 4 aircraft attacked transports in Ajax Bay. 3 bombs dropped and one hangup. 1 hit on Sir Lancelot which failed to explode.
Turning to the Skyhawks, the Navy A-4Q only dropped US manufactured 500lb Mk 82 bombs with ordinary or parachute retarded tails. Max load was four bombs.
The Air Force A-4B and A-4C usual load was 3 x 250kg bombs with the option after 11th May 1982 of a single 1,000lb bomb. The following attacks were made with 1,000lb bombs:-
12th May - Glasgow was hit by a single 1,000lb bomb delivered by an A-4B Skyhawk. 4 aircraft attacked. 2 bombs dropped. 2 aircraft shot down by Sea Wolf on Brilliant and another crashed in sea taking avoiding action. Bad luck on part of Glasgow saw her Sea Dart system fail at the critical time and her 4.5in gun fail after 8 rounds.
21st May - 5 x A-4B attacked the frigate Argonaut. 2 hits on Argonaut that didn't explode. She was very lucky as one came to rest in her forward Seacat magazine, knocking the warheads off several missiles in the process.
23rd May - 4 A-4B attacked Broadsword & Antelope. 2 hits on Antelope that did not explode. 1 aircraft lost and two others badly damaged.
24th May - 5 A-4B attacked transports in Ajax Bay, hitting RFAs Sir Galahad (failed to explode), Bedivere (glancing blow) and Sir Lancelot (failed to explode but see above under Dagger)
I could go on but time is pressing. Coventry was sunk by 3 x 500lb bombs delivered by a Skyhawk. At Bluff Cove, Sir Galahad and Sir Tristram were hit by US pattern Mk 82 500lb bombs. Similarly other ships were hit and damaged by 500lb bombs.
An awful lot has to go right for the Argentinians (weather, aircraft not going u/s, finding more targets, more aircraft bombing successfully etc ) and a lot more has to go wrong for the RN (more weapons failures etc) before any RN vessel is going to be able to be hit by 4 x 1,000lb bombs as you claim as possible.