Could Santa Cruz have turned against Philip II?

Would Santa Cruz hoist another flag or simply refuse to serve?

He is imagined as more likely to act independently, with a hypothetical rebellion supported by experience at sea and on land.

Alex Clarke imagines Santa Cruz as a commander willing to follow his own course rather than accept Philip II's direction. The hypothetical possibility extends to leading a rebellion and having a serious chance of winning. Naval and amphibious ability would be only part of the basis for that judgment. Experience commanding on land would also matter in a confrontation with the crown.