I think that it would increase your chances, but just slightly, since it only involves one class that you weren’t allowed to take. But I think it is important to mention it because it relates to your major, and admissions needs to know that you wanted to take it.
A few years ago my S1 was accepted to the UC’s with only a few AP classes, even though his high school offers more than a dozen of them. I think one of the factors that helped him was that he explained on his application that the prerequisites that his high school required (but no longer require) for taking certain AP classes had kept him from signing up for some of them. I think the high school later changed its policy because they realized that their effort to protect kids from taking on more than they could handle was making it too difficult for them to compete with kids from other schools. I am always amazed when I see posts from students on CC that list more than one science or math class in the same year because his high school still doesn’t allow that.
One thing you might consider is taking a community college class in one of the a-g subjects over the summer. I think community college classes are regarded by admissions as similar to AP and IB. Sometimes it is easier to do well when you are just concentrating on one subject at a time.