Why would anyone in their right mind want to allow notifications? Anyway, I'd rather have a permanent way to get all browsers to not show all those stupid tiles on their home page that show every website one's visited since Hector was a pup.
Like most seemingly useful browser plugins, Chrome notifications are utilized by the aggressive SEO and online marketing and sales communities for commercial websites. Unfortunately, also like most seemingly useful browser plugins, naughty folks are utilizing the heck out of them to achieve less noble goals than increasing sales. Advice: Don't use this feature at all. Rather, use a separate trusted RSS client to subscribe to feeds for updates from websites you are interested in. This keeps you from becoming a victim of malware and also keeps Google away from valuable data you freely send them by signing up for all those notifications. Your site of interest doesn't have an RSS feed? Write their webmaster and remind them this is the 21st Century. Anyway, Chrome Notifications are made possible by the same tech so more than likely, you can't get updates either way. Wondering why all the concern? This sentence from most of the 2012/2013 publicity Google received: "Google is integrating their notification center with Windows operating systems." 'Nuff said.