You could, but I wouldn't do it.
A Master Page is about reuse of design, while a BasePage is about reuse of logic. It's common to have more than 1 MasterPage in a project for various style related reasons, while you typically only have one BasePage you inherit from. This would mean you need to duplicate your code in multiple master pages instead of in a single base page.
Also, it doesn't feel right. Your Web Pages inherit from Page (or from the BasePage in between) that provides the Title so it makes sense to make the class itself responsible for checking its title and other actions you may add to the master page.
So, yes, you could, but I wouldn't do it.
For a similar discussion: Base Page and Master Pages