The sinus infection you get may cause the whole body immune system decline which may directly cause your eyes to feel dry. What's more, the throat and eye nerves system are interlinked. The eye floaters caused by the dryness and weak immune system will be followed with the sinus infection.
No, it would not cause eye floaters due to sinus infection. Eye floaters are a common eye condition and almost every person live with eye floaters and ignore them. They are small moving spots that appear in your field of vision when you are looking at something bright, such as white blackboard. Aging is the most common cause of eye floaters, which is frequently after 70. Or people who are too anxiety or stressful would cause it as well. However, there is no evidence proof that sinus infection relates to eye floaters and has any influence to it.