I'm not finding a problem with my cheap clip-on mounted on the headstock & reading a low B on a solid electric. If it is an issue with the one you get, bridge plucking &/or a 12th fret harmonic can help give it a more palatable signal.
Love that cheap little thing!! It's great when working on a bass (setup or restringing). And it's fun at acoustic jams; just clip it on the headstock of a guitarist who INSISTS he's in tune.
Eventually you'll love a pedal tuner. The mute function is very handy onstage (wished more people used it

. When you get looking, compare the Boss' reading accuracy with the Korgs.