Yes, generally speaking, high blood pressure can make your eyes become red. As we know that when you have done something which can irritate the nerve system, it will make the blood pressure higher. In this way, the blood will flow to the eyes and then make the high eye pressure. As we know that, if your eyes suffer from high eye pressure, it can make the bloodshot to eyes. So at that time, you can say your eyes become red. Anyway, if you have high blood pressure, you should be more careful about it. Or it can be dangerous, not only to your eyes, but also other parts of your body.
Yes. It is possible to cause red eyes because of high blood pressure. One of my friend said that his father suffers from red eyes caused by high blood pressure. Some people also called high blood pressure as hypertension in a medical way. If you have such problems, you'd better see a doctor and do something to reduce your blood pressure. Best wishes.