Would depend. Edward IV dying with an underage heir and an ambitious brother was a perfect storm. Even if Edward had lived only until the end of 1483 - long enough to see Elizabeth of York married to Emperor Maximilian or that Marie of Burgundy's death was avoided and so Liz was due to marry Charles VIII - things would be different. Deposing a king who has zero allies abroad is a VERY different matter to deposing an underage king who is brother-in-law to the future emperor or even an adult king (had Edward IV lasted until 1486/87)
Empire would not matter much as it was unable to project it's power to England, but I agree that Liz being married to Charles VIII would change everythings.