Ugh. I just realized Magento won't let me use the PHP code easily.

Is there any other way of doing this?

I'm going to hand it off to a magento guy, but need to be sure it will work once they figure it out.

Will this work for the Automatic pop-over with the colorbox?

Like, if I have set it to pop over at 5 seconds in the webform builder, will it still popover if the cookie isn't set?

A different approach will be needed for the delay built into the form builder. You could use the cookie code to echo the script that is setting the delay for the popup if the cookie isn't set it will echo the script into the page and if the cookie is set it won't. You could also set a cookie with javascript.
http://www.w3schools.com/js/js_cookies.asp