If you define "space junk" as any human artifact anywhere in space serving no useful purpose, then Starman has become space junk, but so have a number of NASA or other space agency probes that have either malfunctioned, or exhausted their propellants and/or power supplies (RTGs), so the Voyagers are destined to become "space junk" in interstellar space.
If you define "space junk" as a synonym for "orbital debris" (human artifacts in Earth orbit serving no useful purpose, as is usually the case), then no, Starman is not because it is not in Earth orbit.
Junk in space only matters if
- It has the potential to collide with or crash down upon something that matters to you
- It could introduce some form of contamination into a target of scientific study e.g. microbes on Mars.
Orbital debris matters because there is so much of it.