Just having a Freenet connection does not get a warrant — though there are researchers who use some fishy statistics which may be reason not to run a very fast node in the US (because running a fast node provably causes false positives in their statistics).
I think you might underestimate how easy it is to get a search warrant, paticularly in the US. This isnt the standard for arrest, let alone conviction. A cop saying "the machine regularly connected to a suspect network" is more than enough for many judges/magistrates... most of which dont know an IP from an IPA.
For some more details, see https://freenetproject.org/the-discredited-levine-2017-appro... and the links therein.