Not if you do it right. And web sites such as whatismyip.com explictly don't mind if you query their site. They even give instructions on how to do it via scripting:
http://forum.whatismyip.com/f14/our-...on-rules-t241/
And I bet they have firewalls and what not in place to prevent anyone from overdoing it.
So if you follow their instructions and let your automated script hit this URL: http://www.whatismyip.com/automation/n09230945.asp
... then nothing bad should happen. That URL will only spit out your IP address and nothing more, so the traffic that a script would be causing is very very small.
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