I am also on the same page as Chris. Not a great idea for emergency purposes, though I suspect my reasons are different.
Keep in mind that any putative PSA use of the net comes along well after a great many users have been so bombarded with advertising and spam that ads are treated as the very antithesis of "public service". Long enough that an entire industry has evolved with respect to the tactical blocking of ads, banner, pop-up, or whatever. So there is, first, the matter of whether any recipient would actual get to see the PSA.
Second, there is the matter of using one provider. We'll set aside for the moment the political PR matters arising from a monopoly by a software company on the public dime. To simply assure that people are reachable, government would likely need to stay on top of what search engines or potential home pages people are using (and while Google is king at the moment, things WILL change), and make sure there are ads on all of them, and that there is a means to circumvent blocking that works for all of them. And forcing an ad to appear suddenly on the net seems rather unlikely.
Then there is the matter of the digital divide, although this is less a problem, day by day (familiar with the $25 raspberrypi?). Then there is the matter of power outages. I have a little battery/windup radio I can use in emergencies. I even have a battery-operated TV, that'll run off a car battery. I don't know what people would do if the power is out. Yes, some folks will have fully charged laptops, netbooks, or tablets, but not everybody's device will be charged, or have a charge that will last long enough. And just what did you think those wi-fi routers ran on, love?
So, PSAs of a non-emergency nature? Sure, if they buy PSA time on tv, then why not high-profile websites? As an adjunct to an emergency warning system, or as the main emergency warning system, I think it just has so many flaws as to be a source of risk itself.
For the time being, I think the traditional radio and tv interruptions are likely the most dependable we have.