If London actually fell, then that is all true–the Allies are paralyzed. A US rescue plan would require a KGF fleet and cross, which requires Ichabod’s Atlantic investment from get-go (because you don’t know what the J plan is necessarily). We just discussed using 102 to shuttle more stuff over there and attack the Germany fleet, but this only works in the channel and London has to die in the process (because you don’t have an LZ if London stands and japan hasn’t attacked you yet). The rescue with ground units will be more challenging (because you didn’t cross in the face of all the german air ready to Sea Lion and facing west).
All of that is belated thinking; with a proper turtle of 6+1, bringing all that can gather in London, followed by another round or two of part spend should make UK very costly to take over and Germany may not even try it. If he surprises you with a rapid build of transports and strategic bombing, then you haven’t played UK very often; Germany can change its plan at any juncture. The UK in the Global version has crap money but its enough to prevent disaster.
The rescue plan is more for the situation where J3 J4 and later turns where the US is mostly focused on KJF and so only has a limited amount of stuff off Gibraltar. Otherwise, the Germans after turn 5 will not be able to attack (or even move on) UK without inviting a counterattack from the substantial US/UK fleet that has gathered to KGF. At that point any US fighters (there are at least 6!) could have landed, and Sea Lion even with 100% commit should be a bust.