Yes. This will be short -- you need to understand the code you're working with because this technique is one of the most powerful ones Joomla affords you and there is basically no documentation of it apart from the code itself, so do it only after tracking through the code and understanding the ramifications.
HTMLHelper has a register method you can call to register a routine of your own with it.
Once this gets executed, any call to JHtml::_('react') will execute the loadReact method in the class MyClass. The basic idea is it keeps a list of keys that point to methods it needs to call, none of which are required to be members of itself. Then, when told to call that key, it looks it up and executes it. It's the same mechanism used to load bootstrap and jquery today.