I believe the completeness of the set is irrelevant when compared to price to let go when it comes to flipping.
Same principles as buy low..sell low...buy high...sell high. Priced right, there's no problem letting go any watches. It's just that what other ppl think as a "right price" that is the problem.
Service paper from manufacturer will do the job.
But for 'presentation' wise, full set with box and paper look more complete and easier to flip.
I totally agree with the bold part.
Priced right... sometimes when you price a watch right considering the completeness and condition, other might not agree with your valuation and tend to try to go lower and lower...

Some even worse, list at a higher price that what the market is willing to accept and hope some waterfish gets hooked....

As to your question, I would pay a little more for a full set.
For Rolex however, official service papers is good enough.
And yeah, you can't wear the box and anchor or manual out anyway... just for kesyiokan sendiri knowing you have a full set.