I agree that you should settle it, but only assuming there is no unsettled contiguous land and you're financially stable enough to invest in growth, since it will take some turns in the red before this pays for itself. The reason not to have marginal cities is that their civics cost you, but with an island surrounded by coast and a food resource to help it grow fast, it will quickly generate excess cash and take care of that problem. One problem is that you'll have very little production to go toward the lighthouse and work boats you need ASAP (and the granary and courthouse you need after those). So without any intervention it will be interminably slow to become functional. You might consider a little slavery to get the ball rolling. Or investing a little cash up front with universal sufferage. Once you get the work boats and/or light house and have spare population from the fish, you can use some of your population as production specialists.