Accessing content from third party as native posts in WordPress

Simple answer is “no”. Whatever the API you might use it will be too slow to return a page in a timely manner, unless you have the other HTTP server on your LAN, in which case you should just access its DB directly.

What you can do is cache the “external” content in your DB and serve it the “normal” wordpress way. It means that instead of overriding the wpdbclass you will need to write code in “higher layer” that will be responsible to sync items from the remote site whenever it is needed.

Other obvious options are to use iframes or oembed to embed the remote content in your wordpress pages.