The general principle is sound but the engineering is rather a problem. Assuming the launcher is solved (railgun, light gas gun, whatever), and a giant dish to pick up the even tinier then usual signals (maybe the DSN is already enough even, but the US already knows how to build an Orion satellite, so a giant space-based dish isn't impossible), what I would guess to be the sticking points would be the probes themselves.

Each one needs whatever sensors, but more importantly, the auxiliary stuff to last years or decades in transit: in particular power supplies, heaters (=power!) if you can't make your electronics survive constant cryogenic temperatures, as well as comms amongst themselves to organise the mesh and high-gain comms back to Earth.

Maybe the worst of that could be solved with a nuclear power supply and then it's basically "just" radio and software design.

I also don't think you'd use onmidirectional mesh comms, you can get a lot of milage (literally) out of a phased array that can steer the beam at each target, plus it also becomes a bonus multistatic radar network.