They do, generally speaking. But the Saints plan for certain scenarios. But it comes down to the grades. Bowers is graded very highly so that complicates things.
I can virtually guarantee they have these scenarios all mapped out for if they remain at 14 who they'd take in every single scenario. That's really as simple as putting together a top 14 and saying to yourself "I will take whoever the highest player remaining is once we come up."
I think the complicated/long discussion part comes when they have a very highly rated player that starts to drop past their grade bubble and they need to decide whether or not they should trade up for him.
I am sure they have 1 or 2 guys like this that they can see dropping and have already put out feelers on what it would take to move up a few slots with certain teams.