Hi,
I don't think you will be able to do this with the standard app.execDialog() or app.alert() dialogs as the timer is paused when the dialog is displayed, but you could make a subform visible, so that it looks like a popup.
This sample uses that technique to display an alternative date picker, which is really just another positioned subform popping up.
Adobe LiveCycle Designer Cookbooks by BR001: An alternative Date Picker for LiveCycle Designer forms
Bruce