Yes, it would have connection with that. When you have a deviated septum, which would cause sleep apnea that deprives people of proper sleep, preventing you to enter REM sleep. It is way serious because sleep apnea would make you feel tired all the time. Your dark circles under the eyes are probably the result of having no enough sleep at night. In order to solve this problem, you should check for allergy causes, and a deviated septum surgery can fix it.
Well, generally speaking, deviated septum can cause dark circles under your eyes. For example, according to some experts, It could occur if sleep apnea appear or you're just not breathing well while you're sleeping. Of course, you can have surgery so that it can help to reduce the appearance of dark circles. But on the other hand, to reduce the dark circles under your eyes, there are also some other things you should pay more attention to. For example, you should stay away from Caffeine. As we know that Caffeine, similar with sugar, is also a stimulant for lessening your sleeping hours this will then result to dark circles. And you also should know that dark circles can be due to lack of sleepless and the bad diet habit. So just drink enough water and have good rest. I think they relieve your symptoms.
Yes, it can. If you have the deviated septum, you must have the difficulty in breathing normally which may use the mouth as the help. However, the nose and eye nerves are interlinked which may directly cause the eye problems. The not well blood circulation may easily cause the dark circles under the eyes. If you want to prevent it, you'd better treat the deviated septum first.