No. ngrok only tunnels traffic, so it can’t actually serve the HTML file for you.
You can, however, serve a directory of files very easily. One of the quickest ways to start a server is with python. From the command line, cd to the directory containing your HTML files and run:
$ python -m SimpleHTTPServer
Or for python3 (not installed by default on OS X):
$ python -m http.server
Then, in another terminal, run ngrok.