I want to build a wrapper web part which will have properties. These properties must be consumed by jQuery functions and support its consumer webpart. Can we do this?
jQuery runs entirely client side, so it can consume anything which ends up in the markup of the page. It doesn't matter what you add to properties on the development side if those properties aren't available in the page client side.
Keep in mind that you can also use jQuery's AJAX function to query SharePoint's Web Services or read any URL-accessible file, though I don't think that helps you here.