There might be an add-on for this, but if not, you can use the Greasemonkey extension and a userscript. The following script will pop the window up (give it focus) when an alert is fired on a Google Calendar page. I only tested it a couple times, and it certainly could use some refinement, but it might help.

// ==UserScript==
// @name        Google Calendar Alert Alert
// @namespace   YourNameHere
// @description Bring Google Calendar window to the front when the page uses the alert function
// @include     http*://www.google.tld/calendar/*
// @grant none
// ==/UserScript==
var nativeAlert = window.alert;
window.alert = function(msg){
  window.focus();
  nativeAlert(msg);
}

What the script does: it saves a reference to the normal alert() function under the name nativeAlert(), then it overrides the alert() function so that it does an additional thing, which is to give the window (tab) that calls the alert() function the focus, popping it up in front of your currently active application.

I don't use Google calendar, so I don't know whether this will lead to lots of other pop-ups. If so, you might need to add some code to analyze the msg text to make sure you only pop up the window under the right circumstances.

Thanks, but that's a bit too "non-standard" for me to mess with at work. I'll stick to chrome for mail and calendar for now. Thanks for the help though.