If Elizabeth had died, would Mary have been Queen?

A question anet the Tudors, if you go in for counterfactual history:

What would have happened had Elizabeth I died early, in the 1570s-80s, say? Let’s put it right after Catherine Grey’s death. So the only adult in England with any royal blood was Mary Stuart (who, deposed in Scotland, fled there in 1568).

Would the English have found it necessary to offer her the crown? Would she have refused it unless they agreed to reconcile with Rome? Would there have been a Protestant uprising? Would she have invited her brothers-in-law, Charles IX of France and Philip II of Spain, to help her suppress it? (Or another brother-in-law, Henri of Navarre, to help her compromise with it?) Would she have remarried – surely yes – and if so, to whom? An archduke? The frog prince? Norfolk? (executed 1572) Would she have provoked a war with Scotland to recover her lost throne? (Surely yes.) Would the civil war of her grandson’s time have occurred sixty years earlier, and if so, with what result – considering the survival of Catholic feeling in much of the country?

Mary’s political judgment was so generally bad and her imperious temper so uncompromising in later years, I can’t envision her steering through the shoals successfully – but then, I don’t like her. (And her title would never have been so secure among Englishmen as were the titles of Henry VIII’s daughters.)