Metal primer does - or is capable of doing - three things. One - it bonds to the metal in some chemical or physical way that the finish coat doesn't, thereby making the finish coat stick better. Two - it provides a nice, flat, even color under the finish coat, making it easier for the finish coat to cover. Three - it seals and isolates the surface of the metal, making any sort of corrosion or other deterioration less likely. The answer to MontanaCowboy's question really depends on which of those attributes of primer you're talking about.
Category Three is pretty much irrelevant in the context of model parts, which are generally made of brass, nickel, or stainless steel - all extremely stable metals. (
Unpainted brass and copper fittings ought to be given a coat of clear lacquer, to keep them from oxidizing.) Figure painters and ship modelers used to prime "white metal" castings in the hope of warding off "lead disease," but nowadays lead is rarely if ever used in hobby products.
As for Category One - my observation has been that modern hobby paints generally stick acceptably to metal without primer, provided they're applied carefully and handled carefully afterward. Acrylic paint, in my experience, can be brushed or airbrushed onto photo-etched parts effectively as long as it isn't thinned too much. (The same consistency that works for plastic should work for metal.) Primer (that's genuine, honest-to-goodness primer - not just another color of the finish paint) will, however, make the finish more durable. Parts that are going to be handled, in particular, will benefit from being primed.
Whether that makes any practical difference or not really depends on the circumstances. I can't see much point, for instance, to priming the tiny detail parts that go inside an aircraft cockpit - especially if the canopy's going to be closed. The same goes for detail parts on a model that's going to be kept in a glass or plexiglas case. If I'm reasonably confident that the finished product isn't going to be handled on a regular basis, I generally don't worry about primer.
One point to remember: acrylic paint gives the impression of drying extremely fast, but that's slightly deceptive. As a chemist friend explained it on another website, acrylics dry from the outside in. The surface of a paint job may feel dry within a few minutes, but it may take several days for the paint to achieve its maximum "grab" onto the surface. (The same thing is true of latex house paints - as my wife and I have found out the hard way more than once.) Acrylic paint may seem like it's easily rubbed off initially. In two or three days the finish probably will be quite a bit tougher - but not as tough as if a coat of primer was under it.
As for Category Two - primer can be quite handy in establishing a base
color for the finish coat. This is especially true if the metal part and the adjacent plastic parts are of radically different colors. If you stick a brass detail part to a black plastic part, it probably will take quite a bit of paint to eliminate the difference in color. In this sort of paintwork, of course, it's vital for the paint to be as thin as possible, so it doesn't obscure any etched or molded details. Depending on the part, the brand of paint, and the way it's applied, you may well find that a thin coat of grey primer followed by a thin finish coat will give the best compromise between "thinness" and coverage.
Figure painters routinely use grey (or sometimes black) primer on metal and plastic castings to avoid any possibility of the metallic tint showing through the finish coat. They find that black primer, carefully handled, gives a subtly different character to the finished product than grey primer.
My main interest is ship models, and I've used photo-etched details on quite a few of them. I generally don't bother with primer. I find that a coat of Poly-Scale acrylic generally gives a good, even finish - though I usually have to go back a couple of days later with a fresh pair of eyes and touch up some spots where the metal's showing through. For a variety of reasons that have nothing to do with paint durability, I make it a habit to touch the finished models as seldom as possible. I've never yet known any paint to fall off a piece of photo-etched metal because it wasn't primed.
For white metal castings I'm a fan of Floquil grey figure primer - in either the bottle or the spray can. It's a nice, neutral grey, goes on extremely evenly without obscuring any detail, and provides an excellent, matte surface for virtually any kind of finish coat. It works fine as an undercoat for acrylics.
That's my two cents' worth - and probably considerably more than MontanaCowboy wanted to hear. Sorry about that.