To be clear, "self-replicating probe" includes all technologies that can transport, at a minimum, human genetic material, a record of all human science and technology to date, and creche-building technology to a distant star. So a few grams or kilograms of bootstrap molecular nanotechnology, computing material, shielding, some form of reaction engine, fuel for deceleration, and fired by the hundred from a solar-system-wide array of magnetic accelerators or accelerated by lasers. More likely the human genetic material will be absent in favor of emulated human minds.
Or think about actual humans, something large that we'd recognize as a starship, and a vast amount of antimatter. Much more spectacular, and much less likely, because of the amounts of energy involved in getting the job done - and all that just to ship things that could be build on site.
The point being that even if you say that we'll never build self-replicating technology (which is essentially the same as being a vitalist) then given the time scales involved - if every step in the probe network takes 1,000 to 10,000 years of resting time to build a complete organic human civilization before kicking off the next series of probes - it still requires a short time span to visit all stars in the galaxy in comparison to the age of the galaxy.
You're still making ground assumptions that this kind of technology turns out to ever make sense. If we invent transdimensional warpgates in 50 or 500 years, there may never be a faction left over that wants to play with steam-powered genetic plagues.
The idea that you can seed the universe with civilizations in the manner described is highly dubious. You're assuming someone advanced enough to do this yet primitive enough to want to do it and that "it" works at all. Suppose that the galaxy produces one star system in a thousand with a suitable planet, and the seed has a one in a thousand chance of actually producing a successful replication. (Both of these one in a thousands seem to me to be quite optimistic.) The equations look a lot less deterministic.
Or think about actual humans, something large that we'd recognize as a starship, and a vast amount of antimatter. Much more spectacular, and much less likely, because of the amounts of energy involved in getting the job done - and all that just to ship things that could be build on site.
The point being that even if you say that we'll never build self-replicating technology (which is essentially the same as being a vitalist) then given the time scales involved - if every step in the probe network takes 1,000 to 10,000 years of resting time to build a complete organic human civilization before kicking off the next series of probes - it still requires a short time span to visit all stars in the galaxy in comparison to the age of the galaxy.