Treble clef and musical notes

No!

' <== Treble clef

It was very practical but, in reality, these notes were written an octave too high: if another instrument (piano, violin, flute...) played the notes of melody a below, one would hear melody b. By placing an 8 beneath the treble clef, it warns: "beware, these notes are written an octave above those that are actually heard," and all instruments will play it like the guitar, without any octave difference:
After adding the low E string around the year 1800, it quickly became evident that writing music for guitar in the treble clef 8 required using many extra lines, and it was challenging to write music for three voices or more. There were attempts to use two clefs, like on the piano, but in the end, nothing changed. And that's a shame: judge for yourself by looking at all the notes of the current guitar written on two staffs, then on just the treble clef 8: