I've been thinking about the Sarha Jennings question. What you wanted to know is would James have fled if Anne hadn't gone over to the other side? I'm not sure of the exact chronology offevents, but it seems to me that Anne's desertion was a sign of the hopelessness of James' position (the size of Williams invasion force and the lack of support for James). So her act was a symptom rather than a cause of the predicament. :-/
Didn't you also say that Prince George had a say in this, rather than it being the influence of Sarah?
It's my understanding that George was firmly under the control of his wife and the Churchills, particularly John. I don't think George was really involved in Anne's decision to desert her father. When he himself deserted James, he did so in the company of John. George remained loyal to John throughout his life, long after Anne and Sarah's friendship came to an end. He even backed John to Anne and backed him in the House of Lords.
I don't know if removing Sarah would avert the Glorious Revolution as a whole, but it might have kept Anne loyal to her father, thus removing her prestige and approbation from the Whigs and John, who made use of her approval to win people in general and the army in particular over to William's side. Anne's belief in the warming-pan story carried a lot of weight; without Sarah, perhaps she wouldn't have given the idea as much credence as she did. Anne might even have been forced to attend the birth of her half-brother as a witness instead of leaving town in Sarah's company.
The most important thing that Sarah's removal might have achieved is that the army might have stayed loyal to James. Without Sarah, John might have stayed loyal to James, or he might have lacked the clout and prestige to organize the mass desertions. A major reason he was able to organize the mass desertions was because of his close ties to Anne through Sarah. Remove those ties and both officers and troops might refuse to follow John's lead.
If James had held the loyalty of his army, he might have decided to fight William rather than flee. This would have resulted in civil war, which James probably could have won, thanks to William's poor generalship, the xenophobia of the day, the superior size of his own army, and the help and backing of Louis XIV.