What area of Proxima Centauri would need to be occluded for the effect to be observable on Earth? One of ideas of how Breakthrough Starshot could communicate data from Proxima Centauri is to have a massive swarm of the solar sail powered craft to pivot (with their sails) synchronously, taking either 'sideways' or 'head on' orientation to the star - in effect either obstructing it or revealing for an observer 'behind' - on Earth. If the swarm is big enough, it would cause an observable dimming of the star - and timing the pivots right it could encode data in the star's visible luminosity.

The primary question of viability of this idea lies in 'how big a swarm?'. What percentage, or what absolute area or a star like Proxima would need to be occluded for the effect to be observable? We can notice transition of exoplanets quite reliably so that would be the upper bound, but what's the smallest object area that would make a detectable difference?
The photometric precision achieved by satellites like TESS is around 100 parts per million. The original Kepler mission achieved a bit better on bright stars - maybe 20 ppm, but the question of precision may be moot since stars themselves are quite variable;  McQuillan et al. (2012) https://arxiv.org/abs/1111.5580 suggest that the floor level of intrinsic variability in M-dwarfs may be as high as 1000 ppm.

Anyway, let's assume that a rapidly encoded signal at 100 ppm could easily be distinguished from stellar noise and maybe even be generous and say 10 ppm might be possible. That would mean that this fraction of the stellar surface would need to be obscured.

The radius of the star is 0.15 that of the Sun. So the physical area to be obscured is $\sim 10^{-5} \pi R^2 = 3.4\times 10^{11}$ m$^2$.

The web page referred to in the question suggests that Starshot consists of a thousand space craft with light sail areas of 16 m$^2$. It thus seems to fall short of providing detectable modulation by 7 orders of magnitude (unless I have misunderstood the proposal, which isn't mentioned on that web page). 

There is also going to be the question of the low bit rate and what limited information could be transmitted using such a crude technique. Recall that the spacecraft will be travelling at an appreciable fraction of the speed of light, so won't have long to send their message.

A further point is that I don't think it can be assumed that the trajectory of the spacecraft will be such that they are travelling in a direct straight line 
between the Earth and Proxima Centauri, which are of course in relative motion. 
Thus the spacecraft would approach Proxima Cen "at an angle" as viewed from the position of the Earth some 30 years after the spacecraft were launched, unless the trajectories can be tuned quite carefully en-route.
Even if they were, the parallax motion of the Earth around the Sun would mean that the spacecraft would not necessarily be aligned be when they reached Proxima Cen, although I suppose the launch time and speed could be arranged so that was the case. However, from what I have read, the idea is just to pepper the inner au of the Proxima Cen system with these 1000 spacecraft and so only a few of them would actually be lined up so that they could obscure the star as seen from Earth.