Using CI will make your websites more robust since it builds in a design to the way a site is made. jQuery and SQL are just other technologies and both can fit on the side if you want (as Johan said you don’t have to use Active record).
Please remember CI is just a php framework, in the end its just php code. I can’t see any negative points to using a framework other than a slight increase in loading speed (but where talking 1000s of a second, nothing). And for that negative point you get a maintainable well designed site.
Even if you only used the ideas of views and controllers in your website and didn’t touch the database stuff or models or other libraries, you would already be in a better position than you are at the moment.