Here's the concrete screenshots and a save you can test out yourself (f49b just base game).
I set up the scenario through tag switching, turning AI off, giving research and giving equipment.
Before running the save turn the AI off so it doesn't do anything stupid (open console and use the "AI" command).
Cuba has ~200 FTR on their CVs are are entering battle. Cuba has 1.9k land based jets on AS in the Caribbean to really drive home that they've got supremacy. Cuba has a radar in range.
USA has ~150 NAV on a NS mission coming from carriers anchored in an adjacent seazone, of which ~50 get to join the battle due to sortie efficiency.
Here's screenshots of the results with some annotations. On the air stats screen only care about the latest bump on the graph, I was doing other things before this.
All screenshots are taken from USA's perspective.
The battlefield so it is clear what the scenario is:
Taken when Cuban fighters are depleted:
Next sortie from USA:
Battle's end- NAV never damaged boats because of Cuba's AS in the region:
If Cuba doesn't have AS in the region they lose all of their fighters within about a day, and the NAV kill ships:
When I went back to redo the tests for these screenshots I realized that the NAV on air missions replenishing is one of their huge strengths. I think there's a critical point in numbers where NAV just slaughter FTR, and since NAV replenish they'll eventually whittle them down to that point like in the scenario where CUB has air supremacy. It'd be especially useful in long battles.
kendric is also correct about how this strategy works in regards to keeping the carriers on hold safe. You just need your fleet doing a mission in the area and they'll jump in to save the carriers as long as they aren't in another battle. I bet having air missions also increases your overall surface detection.