No, the dots probably don't have anything to do with his illness. The dots are probably supposed to reference some form of African body paint from real life.
(Fair warning some of these pictures in the links below may not be safe for work.)
https://talkafricana.com/traditional-african-face-painting-designs/
http://artreact.blogspot.com/2012/01/art-of-body-painting-has-been-practiced.html
https://www.coreybarksdale.com/art_stories/african-culture-face-and-body-art.html
https://www.vice.com/en/article/laolu-senbanjo-beyonce-nigerian-body-painting-artist/
It's hard to say exactly WHAT Oda's trying to reference with the dots. There's a lot of reasons why different cultures in Africa use body paint. It could be "war paint" or it could be a symbol of some religious significance.
Since the dots are white, that kind of implies that it's for some reason that's "pure" or "good". It could even be "wedding paint" since some African tribes use similar white marks during wedding ceremonies. So, maybe it has something to do with Lili? Maybe this is the equivalent of Imu going everywhere still wearing his old tuxedo that he bought for his wedding day?
But, since this is a Japanese manga, the white could just as easily be referencing some connection to "death". Like maybe this is Imu's funeral attire. So, maybe it's a symbol of Imu still grieving Joyboy or Lili's death?
It's possible that the markings do have something to do with his powers. Especially since, that IS a theme with Imu. What with him giving out Contract Marks to other people to give them powers. So, maybe Imu has a few "contracts" of his own, even if they are taking a different form? But, it could just as easily be some sort of "cultural" thing? The problem I have with it being connected to his powers is that we haven't seen much attention drawn to these markings? They haven't been "glowing" or "disappearing" while he's using his powers or while he's been tanking damage? So, it doesn't SEEM like they're connected, so far. But, they easily could be.
...Or maybe Oda just thinks it looks cool? That's always a option, too.
It's hard to say if it has significance to the plot or if it's just a design choice right now. But, it's probably not related to his disease. But, it's hard to say, one way or another.