Is it possible to use tools like ngrok to create a tunnel into a circle VM running an http server in order to post to it from outside and run browser testing?
You cannot tunnel from the outside in, no - the build servers are behind a firewall for security reasons, and the IPs would be dynamic anyway. However, one solution is to set up a tunnel from the inside out, and then send messages using that channel.
I seem to recall BrowserStack have a bit of software to do this, so you could use this as a start point for research. I’ve not done it myself.