Definitely possible. In the sailing industry it's been common for a number of years. Ideally you take most if not all of the old gelcoat off before painting. This reduces weight and gets rid of having a relatively brittle layer of gelcoat under a much more flexible layer of paint. I'm not as up to speed on this as I used to be but as I recall the ideal is to use a sprayed on primer and color coats of two-part linear polyurethane. This will give you a high gloss, smooth, lightweight, flexible, repairable finish. If you're not up for the job a local boatyard could probably do it for you. Or to save money you might be able to do the prep work and pay to have the paint professionally applied.
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Michael Collins
Sea Kayaker Magazine
michael@seakayakermag.com