Is it possible to use ionic frameowork for regular Web Applications rather than wrapping it in Cordova?
This is possible if you include the components of www/lib/ - This folder contains the core of ionic(the ionic framework + angularjs) and you can proceed from there.
However it's important to note that ionic was built on top of angularjs, specifically with mobile in mind. To get better results for web app development, you should consider using core angularjs(for functionality) and bootstrap3 (for UI).