Can a stress test increase bleeding behind the eye because of increased blood pressure during the test?

Retinal bleeding: Very high blood pressure can cause retinal hemorrhage but it is not common. It would be very rare for the stress test to be allowed to go on with the blood pressure high enough to cause intra-retinal bleeding.

Rare: I would not have this worry that a exercise or pharmacological-induced stress test would raise your blood pressure to the level that you experience a retrobulbar (orbital) hemorrhage. I would doubt that the tester would ever let your blood pressure rise to levels that would cause a stroke.