I’m unclear whether a successful Sea Lion (G1-G3) changes the political situation.
Does the fall of London bring USA and/or USSR into the war or do they still have to wait till USA3/R4?
pretty sure OOB rules are No, they wait like normal in the instance of an attack.�  But Alpha 3 states this:
“If the United States has war declared on it by an Axis power, an Axis power captures London or any territory in North America, or Japan makes an unprovoked declaration of war on the UK or ANZAC, the United States may declare war on any or all Axis powers.”
Um….you’re quoting Global rules. (1st hint tipping you off should have been the mention of Japan & ANZAC…no Japan or ANZAC in Europe 1940)
So to answer the OP question. No, it does not bring USA into the war when London falls. OOB rules are pretty clear on that one (See page 19 -21)