Items sent via USPS can be seized with a warrant. Items sent by other carriers do not need a warrant, just a suspicion.
From here on out, the Constitution says whatever Judicial Watch and the Federalist Society say that it says.
I'd expect packages from out-of-state pharmacies would be deemed "suspicious" and searched. And there's always the handy "exigent circumstances" (translation: We can do anything we want anyway).
I guess the good news is: It's unlikely there are dogs trained to sniff out this specific medication.
They can't do something like x-raying them? I'd imagine that would be relatively easy (e.g. bubble pack with X pills, of a certain size, a certain distance apart), to the point where it could probably be automated.
That's not why the postal service is federal though. Establishing a postal system is a power given to congress in the U.S. Constitution. "To establish Post Offices and post Roads;" Actually having a postal system run by the government was something that predates the U.S. constitution.