We've heard this question a lot because there is still some confusion by some as to differentiating what iBeacons are used for versus Physical Web beacons. By design, the Physical Web was not intended to push messages, so the general answer is no. While the Physical Web will enhance our lives by enabling convenient access to location specific content and interactions with the places, things, or even people around us, it would be a large annoyance if all these things were constantly spamming us with push messages for our attention.
People, places, and things on the Physical Web communicate through the web and there is 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 notify them like the restaurant buzzer example below.
For more info on getting started with Progressive Web Apps and Web Push Notifications, click the links below: