Mayday,
I don't see a problem with what you are thinking of doing, and I have seen it done numerous times. However, if the club you are working on wants a continuous cart path system, it could be a problem.
The reason why most clubs (at least in Quebec) want a continuous cart path system is to be able to send out carts on the course, regardless of the conditions of the course or the weather. If the course is too wet, they can still send the carts out with a cart-paths-only rule applying.
The problems arise when you've got a big rain event on the day you are supposed to have a big tournament with carts. If your cart path system in non-continuous, that means the carts are supposed to cross the fairway at one point. If the course is well drained, it might not be a big problem. If it is not, then you can have an ugly situation where the carts destroy the grass by all crossing around the same spot.
So I would try to do everything you can to avoid this situation, if possible. If not, you can either cross the fairway with the path (which is something I hate and try very hard not to do), or you can route the path so that it crosses from one side of the hole to the other in the rough area in front of the tees or between two tees. I would go with the later if I had the choice, but the visual impact of first option can be minimized with a bit of grading or clever use of the existing topography.
Check with the club officials to see what are their goals with their paths and you will have part of your answer.
Yannick