No, there are no direct tests for using alert and other browser popups. The alert function could possibly be stubbed/mocked in order to verify that it's being called, but as a host function, that might prove difficult in some browsers. Alternatively, you can define your own function, e.g. mylib.dialog("Hello") which by default uses alert, and then test that this function is used as expected.
That's the easy way to do it If you use a library, like Sinon.JS, you can do
The upshot of using a library is
1) You get a richer interface for behavior verification (i.e. was it called? how many times? what arguments did it receive? and so on)
2) Sinon sandboxes the test and reverts the original method after the test has run
Beware that IE not always allow you to override host methods like this. I don't remember if it screams when overriding alert, but you'll notice soon enough