In general, it's always a good idea to use primer because paint sticks to primer better than it sticks to resin/vinyl/whatever. Without primer, the paint will flake off sooner than if you were to use primer. Paint without primer may stay on for 5-10 years, but then it'll start to flake off. Note: Some paints without primer may last 30 years before they flake off -
it varies how long paint will stick due to different paint brands, surfaces, conditions (exposure to sun, rain), etc.
You can use Krylon Fusion paint, which doesn't require primer (it says so on the spray can) because it really bonds/adheres to the surface. Danno recommended it when using Alclad in one of his posts - it's a great paint because it sprays smooth and it sticks like glue. I use Fusion black all the time when using Alclad.
But even with Fusion as an undercoat for Alclad, I *still* use primer. The reason is because with Alclad, you *need* the surface to be smooth in order for Alclad to give off a nice chrome look. I'd read posts saying that the surface needed to be smooth, but I disregarded them, only to see how poor Alclad looks on surfaces with small imperfections. So now, I always make sure the surface is smooth. With primer, you can see all the imperfections, sand them smooth, recoat with a light mist of primer, spray with Fusion, then airbrush it with Alclad chrome.
You may even be able to use black primer as an undercoat for Alclad, which will allow you to skip a step (black paint). I have yet to try it but I'm sure it'd work.
Good luck!