What does a black base color do when painting silver?

This depends upon what type of silver paint you're going to use, as well as the method of application. If you're hand brushing on a standard enamel paint, it is not a consideration. If you're airbrushing on one of the various metallic finishes such as Alclad or similar product, it's a requirement. 

You need to understand the different silvers. Some are silver paint period, may have some fine metallic flecks in their makeup. Others are specifically formulated to look like bare metal. These are largely made up of real metal particles in a carrier base and also quite fragile.

In metalizer paints a gloss black base and to some degree a semigloss black base increase the metal look of the silver. Especially so or maybe I should say all the more so when trying to duplicate chrome. Additionally lighter coats of the silver counts too, you can lay on the silver too thick ( black base or not) and it just looks like silver paint. You need the gloss of the black below to bring on a metal looking sheen or luster.

With plain silver paint this isn't as much of a case, though I do still like black primer as the base because if you don't see the imperfections in black primer it's a good step towards them not showing up in the silver finish.

It's a very worthwhile question, but you may want to consolidate it into one thread for responses.  I think there are three going.

I have found that black base coat may or may not make any difference and doesn't necessarily make it "better".   I typically spray plastic spoon samples with my color over a variety of primer coats to see what I prefer.  In some cases, you can achieve the effect of different aged panels simply by masking off areas of one color of primer and adding another before top coat.