First off !important applies to one specific declaration in a CSS rule. It doesn't apply to a class. So, "no" you can't make a class !important.
Second off, !important is just one part of CSS specificity. You can also use other ways to make a rule be a more specific rule to have precedence (such as referring to an id in the parent chain instead of just the class. When I'm writing CSS, using !important is my last possible choice - I'd much rather solve overrides with other specificity solutions. Usually, if you control all the CSS, this is pretty easy to avoid using !important. If you have to override some CSS that you don't control, then sometimes it is handy.
If your jQuery code is going to toggle a class on the object, then you will have to craft your CSS rules so that adding/removing this class causes the right CSS declarations to have precedence. For us to help you further with that part, you would need to show us the relevant parts of both your HTML and CSS so we could advise on how to solve your precedence/specificity problem.
