Obviously changing the order of holes (not just the sequence) will be more noticeable to members who play the course regularly and are used the way their course 'flows', starts and finishes.
At Kingston Heath we play what is called the "Masters Course" on a Wednesday, so that there are two returning 9's created (it's actually 8 & 10). This allows pre-booking for morning and afternoon fields off 2 tees, and therefor larger fields. The regular sequence has the 6th tee returning to the clubhouse, and the 10th out in the middle of the course.
When the Australian Masters and Open are played at KH, we use that sequence for the same reason. It allows a 2 tee start, which is better for tournament organisers on Thursday and Friday. Our great 10th hole is often then omitted and replaced by 19. The 'Masters Course' is 7,8,9,11,2,3,4,5,6 back to clubhouse 1,19,12,13,14,15,16,17,18
I have taken a few GCA guys to KH on Wednesdays, and I'm not sure how, or if, playing the course this way was an issue. I know a few are confused looking at the card, because the normal hole numbers remain on the card - therefore it looks out of order.
However for me, playing the course this way is like listening to Pink Floyd 'The Wall' on shuffle. It just doesn't work