yes, but they travel slowly and have to somehow (never clearly stated how) communicate back to home. as they spread out, the comms stuff becomes more and more problematic.
If they work anything like any natural or artificial communications system we’ve built, each new “node” would immediately establish a connection to the nearest colonized star system. Light speed delays would still matter, but any important news and communications would get delivered.
A communications network that works with an average latency of five years (the average distance between stars), and an edge case of millions of years would be all but useless. The civilization that started it might not even be the civilization that receives the first message, or even the same species. And what does "important news and communications" even mean with that kind of latency?
Also there is signal degradation to consider. Depending on their broadcast strength, there is a limited range beyond which any signal they send will be indistinguishable from background noise. According to this quora post[0] that limit could be as little as four light years. It certainly would not work on any significantly pan-galactic scale. Lasers would fare little better, they would also diffuse and be absorbed by interstellar material.
Also, at that scale, whatever message gets sent may no longer be relevant, or factual, by the time it's received. A lot can happen in a million years. It's difficult for me to think of a message worth sending that also doesn't matter if it takes longer than the time it took humans to evolve to get from point to point.
I think a better way to think about this is: what would humans do if they had a few crucial pieces of technology? Assume you have computers advanced enough to self-replicate and carry out some pre-programmed set of goals creatively (this is essentially required for Von Neumann probes to work, and doesn’t seem wildly out of the ballpark for even humans in a few hundred years.)
My guess is that we would optimistically assume human survival and build a network capable of exploring the galaxy without us. Since lightspeed delays make real-time communication impossible, individual nodes would be programmed to replicate and explore, following a specific set of parameters. They would report their findings back to some central hub if they found anything interesting, which would probably be only rarely. No doubt for very surprising findings (eg advanced intelligent species) they’d have additional instructions to enter a holding pattern and observe until they received explicit commands. Which, as you point out, might never come.
I can’t speak to what aliens might do. humans would absolutely build this system the moment they had the technology to do it. The fact that we might not survive to use it would be acknowledged and then we’d do it anyway. If anything we’d see it as a fitting memorial to our existence.
once again, someone suggests that humans will develop (at probably staggering costs) probes that cannot report back to them for tens of thousands of years. how many human civilizations have lasted that long - zero? it is simply not in our interest to do so.
At the point where a civilization can build self-replicating intelligent probes, concepts like “staggering cost” probably aren’t as much of a barrier as you’d imagine.
That's a fair point. If they are autonomous and carrying out a mission on your behalf, perhaps they don't need to communicate back to be useful. Might still leave defense, advance scouting, resource location (a broad search), panspermia, or other possibilities.