Does Unreal Engine have HTTP Post Functionality?

Just asking in regards to creating an API Toolkit with this in the future.

Yes, it does appear to be able to send an HTTP request with the “POST” verb, at least through C++. It seems like they have a wrapper which passes off to numerous back-end libraries, depending on your platform. It looks like you simply use the SetVerb() method as you set up the HTTP Request.

Discussion in this answer should guide you to the appropriate syntax: FHttpModule Discussion

Raw HTTP requests do not seem to be exposed to Blueprints, at least not directly.