It is the easiest possible question to ask and answer -

If daily rotation which causes the day/night cycle ceased to exist, would a person on the surface still experience a single day/night cycle each year ?.

The answer is Yes, they would experience the same day/night cycle that currently happens at the North and South poles where the Sun comes into view on one Equinox, stays in view constantly for 6 months until the opposite Equinox when it goes out of view for another 6 months.

This surface rotation is parallel to the orbital plane and Copernicus, in his original Commentariolus, got it right -

"The third is the motion in declination. For, the axis of the daily rotation is not parallel to the Grand Orb's axis, but is inclined [to it at an angle that intercepts] a portion of a circumference, in our time about 23 1/2°. Therefore, while the earth's center always remains in the plane of the ecliptic, that is, in the circumference of a circle of the Grand Orb, the earth's poles rotate, both of them describing small circles about centers [lying on a line that moves] parallel to the Grand Orb's axis. The period of this motion also is a year, but not quite, being nearly equal to the Grand Orb's [revolution]." Copernicus

http://copernicus.torun.pl/en/archiv...=transkrypcja&

Oh the satisfaction in being able to restore part of that astronomer's work by allowing the older framework for timekeeping to emerge and displacing the Greek system of reckoning that Copernicus and his contemporaries were chained to.