Wouldn't that be the most difficult and expensive way to simply monitor for life or technosignatures? Compare that to simply (relatively speaking) building massive space based optical and radio observatories that can observe every visible star. The light reaching you has already made the trip, you just have to collect it. If you were murderous, you could launch an attack from your home system rather than waiting for the probes to spread from system to system.

Granted there could be some technical limitations that prevent you from observing certain systems but that pool will be much smaller than an entire galaxy of stars.

Also, don't forget that a Von Neumann probe is at a disadvantage when it arrives in a system since you want to send the minimum number of probes to each star and then have them replicate on arrival. If your probe accidentally shows up in a system that contains an advanced civilization capable of detecting and capturing it then you've given away the fact of your existence and your intent along with all the information that can be gained by studying the probe.

So have your replicators approach a system from an unexpected vector; one course correction in interstellar space should be enough.

Also I'd expect the probes would communicate with the homeworld via relays (where they were replicated) rather than directly, so it'd take a fair amount of effort to unravel a replicator network unless you caught one of the very first probes.

And also it'd be conspicuous if there was a volume of space in your network where your probes always failed.

I wonder if everyone is therefore incentivized to not send out such probes, then. Since no one can guarantee they are advanced enough that their probe won’t get captured by someone more advanced who just sends back a scarier probe as a thank you gift.