Earl of Essex Rebellion

In 1601, Robert Devereux, 2nd Earl of Essex attempted a coup against Queen Elizabeth. He attracted a moderate amount of support among the aristocracy (including several people who would go on to be involved in the Gunpowder Plot), and had about 300 supporter with him during his coup attempt. Unfortunantly for him, there was no groundswell of popular support, the Sheriff of London backed out at the last minute and refused to call out the Trayned Bands on Essex's behalf, and Essex failed to recruit the army he'd once commanded in Ireland to join the rebellion, and he wound up being soundly defeated. He was tried and executed for treason within a couple weeks and most of his supporters were imprisoned or fined.

There's two things I'm curious about here:

1. Is there a plausible POD for Essex's rebellion to succeed?

2. WI Elizabeth suddenly dies of natural causes when Essex is almost ready to attempt his coup? Would Essex follow through with the rebellion in order to seize the crown for himself, and how likely would he be to succeed if instead of trying to overthrow a popular monarch, he's trying to fill a sudden vacuum?
 
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