The diameter of the fallopian tube is quite small within the uterine wall. The tube increases in diameter as you move distally towards the opening near the ovary. Permanent proximal tubal damage due to scarring inside the tube is uncommon. In either of these situations the media travels preferentially through the path of least resistance and no longterm pathology is present.
Pathology exists when the nonfilling side is occluded with a mucus or proteinaceous plug.
The nonfilling tube may also be occluded by a pelvic process that should be addressed surgically. If there are severe pelvic adhesions, endometriosis, or tubal luminal adhesions following a pelvic infection then the tube may be occluded all the way back to its origin at the uterus. Such extensive disease is only likely to occur in patients with a suggestive history. The primary downside of trying to conceive for 3-6 months despite one nonfilling tube is that you may delay other appropriate care. In a young couple this may be acceptable.