Reverse iBeacon and Proximity Sensor
Yes, it would work just fine in theory. 

However, it will stop working well when you have too many people (beacons) all in the same area. Each beacon is an uncoordinated transmitter and its messages can and will collide with others. Messages will also be garbled by interference from other 2.4GHz transmitters (WiFi, other Bluetooth devices, microwave ovens, etc). 

Also, at some point you may have a large number of beacons (e.g., 100) and in each interval (e.g., 1s) the receiver will only see some fraction of those (e.g., 50%). While that may seem okay and you might think that you should see them all in a few seconds, it can take a while to see the last few. It becomes a variant of the Coupon Collector's Problem.

The question of where it breaks down is left as an exercise for the reader. Others on SO have reported at least 20 beacons working nearby with no problems, but your mileage may vary. 

In regards to using an embedded Linux computer (Raspberry Pi) to scan for beacons, there's this question on SO and this guy's Github project.