That's one thing that you can do but it's by no means a certainty either way.
Some sites will ignore ICMP packets so that no ping response is given. Some sites will respond to pings even when the web server (or whatever service you're after) is down.
The only way you can be certain that a given site will provide a service is to, well, use that service. Nothing else will be as accurate.
A better method would be to provide a series of steps which would detect where a fault lay, at least in the infrastructure that you can control. For example:
- allow pings to be received and acted upon.
- have a static web page in the web server.
- have a dynamic page in the application server which delivers static content.
- have a dynamic page in the application server which uses the database.
Then your tester client would simply attempt to "contact" those four points and report on the success. Since you would expect your site to be up most of the time, I'd just check the fourth option to see if everything was okay, and do the other checks only if a problem were found.