I can't speak to the davits themselves, but if the deck surface is a cored laminate, I would want to do more with the core than just use caulk.
One way is to overdrill the hole, dig out some core, re-fill with plain/thickened epoxy, then once that has cured drill for screws.
Self-tapping type screws don't get that great a grip in resin/glass though, so you might consider tapping the new material for a machine screw. (Or maybe the davits want to be through-bolted; I don't know what the stresses are on them.)
Marinehowto.com (RC) has good photo-tutorials on sealing off core and bedding fasteners.
I remember DDW (back on a sailing forum) had a slick way where he epoxied in pre-tapped tubes of G10, but that's just extra coolness (and it is nifty).
Main thing to me is to really seal off the core (not solely with caulk) if it exists, and to use fasteners appropriate to the load (whatever those may be since I don't know the load).