You could argue a "report alert window" is simply a folder in Cognos Connection containing newsitems. Nothing would "pop up", though - this is not how the Cognos standard user interface works. If you go into the properties of a report in Cognos Connection and in advanced properties enable the "enhanced user features" option, a user can then ask for alerts to be generated whenever the output is regenerated or if a specific condition is met when the output is generated. These alerts can be via email or could be added as newsitems in a folder. This folder could in turn be displayed in a portlet in a Cognos Connection page or within Business Insight/Cognos Workspace.
Cheers!
MF.