This is possible, in fact, since they will work in the context of the same application, this should not be a problem. You may need to register a new ViewEngine that points to / MvcFolder / Views for your views. The root of the application will still be ~ /, so you might need your routes to take this into account, for example. having something like "MvcFolder / {controller} / {action}", etc. as the routing rules, etc.
MVC and WebForms applications can work side by side without problems. The UrlRoutingModule module will comply with any rules before the request reaches the WebForms HttpHandler, so be careful in routing any rules such as "DoSomething.aspx" as this will be intercepted by MVC.
If you decide not to register UrlRoutingModule in the base web.config, you can register it in the /MvcFolder/web.config file. This will stop any routes that will be mapped outside of / MvcFolder.
Why are you registering the rules in the HttpModule? They will be executed for each request, so you are sure that you do not register rules in each request unnecessarily?
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