Does changing the order or sequences of the holes of a course change it's originality if nothing is done to the holes themselves?
Well, sort of yes and no.
Yes, in the sense that for those playing the course in some other sequence many may not get the same feeling about playing the course for various reasons, perhaps better but probably worse.
No, in the sense that if the club doesn't like the other sequence all they have to do is go back to the original sequence the next day and it's as if nothing happened.
One of the most interesting nine flips was Shinnecock. Flynn designed the course with the nines reversed but they rather quickly changed it to the way it's been ever since and on that particular course it makes a big difference, in my opinion.
Matter of fact, it was even more interesting than that. Initially Flynn designed three separate nines there and the starting hole on one of the nines was the present 14th!
There's even another interesting sequence to Shinnecock. I call it the "Merion Sequence". Start on #14, #15, #16, #17, #5, 6, 4, 18, 1, 2, 3, 7, 8, 9, 10, 11, 12, 13, and your back at the clubhouse. The reason I call it the "Merion Sequence" is it's par 5, par 3, par 5, almost right away (Merions #2, #3, #4) and that's it for par 5s for the round!