I think it's undoubtedly a good investment to spend the time to learn a PHP framework. For one, it'll teach you how someone has tackled the problem of architecting the framework, how to organize your PHP code, and how to handle things like sessions and database accesses...etc...
For the most part, if you are serious about developing web-apps, you will need to use a framework of some sort rather than writing your own framework from scratch.
Some reasons why you should NOT write your own framework:
- You're re-inventing the wheel, when it's been done many times over already.
- You're not very likely to do a better job than an open-source framework, which has been tested and iterated over by many developers.
- You'll spend all your time writing and debugging your own framework than you will spend on actually creating your application.
So yes, learn a couple of frameworks and find one that suits you the best!