Maybe, but I’m not seeing anything that suggests that would be possible.
Here is the technical documentation for how this feature works. The short version is that it exposes some new JS functions that sites can invoke to register various ad related activities. That data in turn gets forwarded by the browser to a 3rd party using a protocol called DAP which can be considered out of band for the purposes of website interactions. I see no evidence at all that uBlock would be able to block the DAP calls, and limited evidence it could effectively block the JS functions.
uBlock works primarily by blocking network requests using a series of rules. Here is the syntax supported by uBlock for defining its blocking rules. It primarily works by inspecting hostnames, although there is some capability to match on things like HTTP headers, or raw text. There is the capability of blocking an entire script element if it matches specific text E.G. navigator.privateAttribution, however doing so is likely to break sites quite drastically. There is very limited ability to surgically remove such things. Maybe if you injected some JS into each page that overwrites the navigator.privateAttribution namespace with stub functions that do nothing (I believe this is actually what the browser does when you opt-out of that feature), but I’m not sure if that’s even possible or if the browser would simply ignore attempts to write to that namespace.
It’s possible Firefox is being “smart” and if it sees you have uBlock or similar ad blocking extensions loaded it disables this feature. It’s possible that there’s some extra tricks uBlock or other extensions can pull to block this at a more fundamental level that just aren’t obvious from looking at their documentation. But nothing in the documentation for this feature seems to guarantee any of that, and it’s frustratingly vague in several areas. Regardless none of that changes the fact that this should have been opt-in from the start instead of opt-out. Mozilla argues that they made this opt-out because they wanted to insure a large enough user base to anonymize the collected data, but that alone suggests there might be privacy problems with this entire thing. This wouldn’t be the first time that a supposedly anonymized data set could be at least partially de-anonymized.