Can taking rhodiola rosea and l-theanine together cause my blood pressure to drop too much at any time (including when standing up)?

Blood pressure. That drops and makes someone dizzy when they stand up means that you need to see your doc because your bp is probably too low. I see that you have thyroid issues also which needs to be factored in. Rhodiola is used to prevent high altitude illness by expanding blood vessels and can lower bp. Theanine can lower bp but primarily keeps one relaxed and focused. Peace and good health.