Here are a couple of suggestions.
1) The loadbalancer can call the page AE.axd
The loadbalancer gets an answer in plain text along the lines of:
SessionCounter=0 Language=english CultureInfo=de-DE AdditionalLanguages= IsInMaintenanceMode=False
It's a call that doesn't leave a session open, and returns some useful information that could be used in further logic.
2) Or try calling a web page that does not exist. This is a simpler test that returns two different error codes that can be evaluated.
For example, if you call http://server/web/pagedoesnotexist.axd you get an error 404 if the webapplication is running.
If not you get an error 503.