pop up blockers will not affect the behaviour of an alert box, but - to paraphrase felgall's oft-cited warning - many browsers offer the option to suppress alerts when showing the first alert. If the user selects this option it makes your code effectively worthless as subsequent alerts will not be shown. Alerts should be used for debugging only, never for live pages.

innerHTML, createElement and css block/none, visible/hidden methods are all better examples of displaying results to the user.