Yes it does, in the sense that aggressiveness determines whether or not you will select a signability risk, or pass for a "safer" player. Any player who says they will sign for slot will sign for slot (and sometimes a little less) pretty quickly. They will never not sign. Anyone who says anything else will either ask for more money, have a risk of not signing at all, or both.
The signability statements really tell the tale. "Wants to be drafted in X Round" generally means that if they are, they will sign, but may ask for more than slot (sometimes a couple of $mil more, though usually less than that). "Undecided, strongly considering playing X other sport" will generally ask for slot money only, but pose a very strong risk of not signing at all (in which case, upping the offer will not cause them to sign- they're just not signing). "May sign if the deal is right, otherwise going back to school" generally means "Will sign, but I'm going to totally bend you over on the signing bonus" though sometimes these guys will just turn you down. "Probably won't sign" means they're going to ask for a bunch of extra money, and are very likely (80%?) to turn you down anyway. "Probably won't sign" kids whose agent/rep is their Mother will ask for 300-500% of slot or more (which you will have to offer to get your Type D pick) and have almost no chance of signing no matter what.