Why not install & configure monit as part of the iRedMail install.
It'll give you process monitoring and management - and additionally will give you service status for the above page.

I have most of the monit script for iredmail for deb if that helps.

Just mailed them to you.

Ah - I setup a new folder under the web folder with a simple file in for the http end-2-end test.
You could do the same with one of the images from the webmail folder.

With these end-2-end tests - it really depends how deeply you want to verify.
The current smtp checks just verify that the port is alive and the process (via it's pid) is working.
I have a test in progress for end-2-end testing smtp - so sending a mail and checking it's actually delivered - but I've not had time to finish testing it yet.

One of the advantages of using monit - apart from ensuring the services are actually running - is that in a multi-server env you can use the mmonit management interface and have an 'at a glance' view of your environment & it's status.