Can a star emit a larger fraction of its total light in the visual range than the Sun does
Surely this is exactly what the V-band bolometric correction assesses. The numerically larger the bolometric correction, the more of a star's flux (as a fraction) is in the V-band.

The Sun's bolometric correction is about -0.06 to -0.11 mag, depending on which sources you look at. Cool stars and hot stars have numerically smaller BCs and emit a bigger fraction of their flux outside the V band.

Some sources put the BCs of A5-G0 stars as very slightly larger than the Sun's, by up to 0.1 mag (e.g. Pecaut &amp; Mamajek 2013).