But, like what isack24 said, it can have a domino effect. If I see a guy in n+1 and in two battles with two others considering him vs another team who is n-2 and in no battles, common sense says that the n+1 guy is going to have a much harder time fending you off. Odds are he's going to have to focus on one or two of the battles in order to win them.
It all depends on if other coaches are paying attention. It seems like some people have the strategy of going n+5 or more to make people guess at who they are really after. It may be a viable strategy... I've never tried it, but I see enough teams do it that it must have some value, but to a lot of coaches going n+ signals that you might be spreading yourself too thin and are vulnerable to have a recruit taken from you.
You have to look at all of the variables, too (distance, prestige, estimated budget, etc), but in a vacuum, you're better off piling on to the guy that's already possibly spread thin and in some existing battles that have dented his budget.