We do not know that. A self-replicating probe not only has to make it to another star system, but it has to somehow find all the materials that go into a complex machine, build factories and smelters and figure out how to get the energy for all of it, and essentialloy re-create an entire technological supply chain. Then it has to send that next probe off with enough fuel to do the whole thing again. And it probably has to send off many probes to account for the ones that don’t make it to a system with the materials to replicate.
Could it be done in the sense that it doesn’t violate any laws of physics? Maybe. can it be done in a way that maintains exponential expansion through multiple generations of unknown trips to unknown systems? That’s a much harder question.
Build a complex, computer controlled flying machine that can be plonked down in some remote area of earth, then replicate itself. How hard do you think that would be? You are going to have to replicate everything from insulation to chip fabs to metal parts. You’re going to have your machine explore for materials and mine them. But of course it has to build the mining equipment. Which it can’t do until it has mined the resources. So you’ll have to send mining equipment along, and when the probe replicates, it has to replicate all the mining equipment as well. But you can’t build the mining equipment without the tools needed to build the mining equipment…
Self-Replicating probes could be technically possible out on the edge of feasibility, but still never be made because the efficiency math doesn’t work out. Maybe it takes so much material and energy to make a true self-replicating probe that it just doesn’t make sense, and it’s more efficient to just send probes out from the home world from time to time. If that’s the case, you don’t get the exponential expansion that makes self-replicating probes such a juicy topic for the Fermi Paradox.
And so it goes. The supply chain for something as simple as a laptop computer stretches into many millions of people and thousands of companies.
It may be that self-replicating probes are technically possible, but in practice so freaking hard and expensive to build, with such a long-range payoff (if any) that only one civilization in a million would bother to even try. So we could have 10,000 civilizations in our galaxy with none of them ever building self-replicating probes.
As of today, they are complete science fiction. We have no idea how to build them, and we don’t know if anyone else has either. To use them as a given “If there were other civilizations we’d know, because of self-replicating probes” is ridiculous.