When I see people using MySQL, it's generally via the PHP bindings. Is it possible to interact with MySQL using C++, or do I need to learn PHP first?
You can use MySQL with many other languages.
You just need a driver, a list is available here.
Yes it's possible. No, you don't have to learn PHP first.
If you're planning to create websites or web services - PHP. If desktop programs - C++. If you need MySQL just to store and analyze some data (a la MS Access) - neither.
There are MySQL bindings for many languages, including C++.