Boring or not, with just one note it wouldn't count as a melody.

Why on earth would anyone feel obliged to fret the strig with a thumb when they'd have four other fingers to use? Plucking with the thumb, now that's different.

No reason it wouldn't be easy enough to play tunes fretting the fifth, provided it was a banjo where there were frets under the fifth. It might sound good on some tunes too, using the fingers to fret the fifth string and plucking with the thumb, while frailing the same open chord on the other strings. Dukcimers get played that way sometimes.

The question is, did anyone ever play the banjo that way in the old days, as those reference books rather suggest, by calling the fifth string "the melody string".