No, vBulletin doesn't have the option to send a notification email for Visitor Messages like they do for PMs.
It would be a nice feature though and I've sent the suggestion to them while maintaining our vB board on another site. They haven't implemented it as of version 4.1.10.
If you want to, you can disable the Visitor Message feature though. that way if anyone needs to contact you they will need to use either the PM or email features (if you've got them turned on) instead.
Otherwise you just gotta check your profile page a bit more often.
(I know...I don't spend much time on that page either unless I'm searching for some of my old threads or cleaning my PM inbox.)