I'm certainly no legal expert, but wouldn't the whole "fruit of the poisonous tree" argument apply to any evidence found after and/or as a result of the MAC address connection?
Second, that applies to illegally obtained evidence. For example, if (in the US) the police tortured someone/broke in somewhere without a search warrant to obtain the MAC, then the fruit of the poisonous tree doctrine would likely apply to the evidence found as a result of the MAC address connection.
Finding additional evidence starting from a vague lead ("the robber was wearing black clothes") is not something illegal, it's good police work.
Edit: by unconstitutional I’m speaking of the US. I am not sure what constitutional protections apply to other country’s citizens, but assume they may be similar.
It just doesn’t apply in this case, because it hinges on bad faith. Incidental evidence found while following some other legitimate trails is admissible.
It would first have to apply in the jurisdiction we're talking about, which in all probability does not...
It has however seen some use in the ECHR , notably against Germany (citing various US court cases):
> the applicant sought a declaration that [...] all items of evidence[...], which had become known to the investigation authorities because of the confession extracted – the so-called “fruit of the poisonous tree” – was prohibited [...] The Chamber considered that there was a strong presumption that the use of items of evidence obtained as the fruit of a confession extracted by means contrary to Article 3 rendered a trial as a whole unfair in the same way as the use of the extracted confession itself.
Gäfgen v. Germany, at 25 and 147 https://hudoc.echr.coe.int/eng#{%22dmdocnumber%22:[%22868977...}
It almost certainly wouldn't apply here though (as there is no illegal act).