You would need to have some technique that would be cross vendor compliant. That is, Apple might put their computers to sleep with one technique, Dell, might use another, Asus motherboards could use another, and some computers will completely shut themselves off. If there is a way for a web browser to "wake" a sleeping machine (and I don't think there is one), but even if there was... I doubt that it would work for every vendor... especially the ones who have the computer shut themselves off.
So I think your best solution is to either require that Agents not be allowed to use computers that go into sleep mode or look into an API that dials phone numbers and relays messages in voice. I think those can be had for around $.30 per call. So you update the screen, wait 30 seconds for the user to click "Ok, I got the message". If no click, then dial the Agent's phone number.
Yes, I admit that this is a silly answer. But given the nature of sleep mode on different computers, I can't think of a more safe solution.