This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
The authors of Struts anticipated that users might want to do things a little differently, so they wrote the components (ActionServlet, RequestProcessor, etc.) with extensibility in mind. So, the answer is yes, you can override the ActionServlet.
To do so, just write a class that extends ActionServlet and then put your class as the <servlet-class> in the action servlet definition in the web.xml file.
Maybe it's just a language thing, but the way you worded your question, it sounded like you don't want to use any of the existing functionality of the action servlet. If that's the case, why use Struts at all? Just write your own framework. If you just want to modify a few minor things about the way Struts handles things, then you're on the right track by extending ActionServlet.