We've heard this question a lot because there is still some confusion by some as to differentiating iBeacons vs Physical Web beacons... by design, the Physical Web does not push messages, so the general answer here is “no.” While the Physical Web will enhance our lives by enabling convenient access to location specific content and interactions with the things around us, it would be a grand nuisance if all these things were constantly pushing us for our attention.
People, places, and things on the Physical Web communicate through the web by design. Because of this there is some emerging technology like Google's Services Workers and designing Progressive Web Apps that will allow users to opt in to push messages from individual websites. This approach makes sense for the Physical Web, where users may only want a few important things to push messages like the restaurant buzzer example below.
For more info on getting started with Progressive Web Apps and Web Push Notifications, click the links below: