That is a good question. The Voyager spacecraft send out detectable signals with a ~20 Watt signal. This is larger than the ~3 W signal that a smartphone sends, but by less than an order of magnitude.

Voyager is at ~130 AU. Alpha Centauri is at ~275,000 AU. With the 1/r^2 decrease in signal, that means the signal from earth will be smaller by a factor of ~3 x 10^6. Now, supposing we have ~1000 of these smartphone probes, this means that their combined signal will be weaker than the Voyager signal by a factor of ~3000. We might imagine that they are somewhat more optimized to send a stronger signal than an ordinary smartphone. Let's say they have a 30 W radio instead of 3 W. This means that they will have a weaker signal by a factor of ~300. This is a lot, but if they manage to build a detector that has a larger effective diameter than the Deep Space Network by a factor of ~15. Given the budget of the project, and the fact that they have 20 years of time to prepare after the launch, this could be feasible.

Looking at the project's website, though, it looks like they are taking the approach of using a laser onboard the probe instead of using a traditional radio transmitter [1]. This would increase the efficiency of the transmission by several orders of magnitude. It might even be possible to detect the signal from a single probe with this approach.

[1]: http://breakthroughinitiatives.org/index.php?controller=Foru...