I know enough to output dynamic content. I'd probably say that's the current extent of my PHP skills but that seems like a fairly limited scope.
Learning as much as I can sounds good to me! It's just a concern that I keep seeing PHP getting bad press.
It all depends on the types of web apps you want to build. How about watching some videos to get a feel of the different solid frameworks and pick the closest to your needs?
Since the backend for WordPress runs on PHP, it would make sense to learn at least a little about the language.
I'm also of the opinion that you should learn as much as you can, especially if you're curious.