As for the Catholics being both numerous enough to rise and likely to actually do so--that, like Parma's frustrated conviction he could and should have prevailed in the Netherlands, is something we don't really know, but certainly there was some doubt Elizabeth could rely on all her subjects to rally to her and not a Spanish-favored candidate for the throne.
Parma might well have landed and then found that the country folk weren't going to flock to his banner after all.
But certainly Elizabeth herself is responsible for much of the retrospective view we have that English people are automatically English first and these sectarian factions second; between her and Shakespeare, the two of them did much of the work of creating English patriotism. Mattingly gives examples of how she "courted" her people into a sort of collective marriage with all of them. The Armada fiasco as it played out OTL had a lot to do with consolidating her position; had things somehow gone better for the Spanish it isn't clear how solid English resistance would have been.
The areas of plausible landing weren't areas of Catholic strength, for one thing.