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.
Sea Kayaker Magazine