How does one render effects with non solid alpha?

I'm a little confused by your terminology. There are two rendering modes in Particle Illusion. Direct, which gives you a white alpha and no transparency, and Alpha + Apply wich gives you transparency. The transparency respects the soft edge of the particles.

If you want to put a hard edge around the particles you have to apply the Curves effect below Particle Illusion, go the Alpha Channel Curve, and crank on it until you get little or no feathering on the soft edges.

The curves adjustment will give you some additional control over the apparent size of the particles and comes as close as you can get to a "solid" alpha.

The Borris FX suite is incredibly complex. I probably spend seven or eight days total just going over the documentation and the tutorials on the Boris FX site before I knew how to do much more than just apply them and load a preset.

Almost all particle effects have an option to generate an alpha channel. Some do it automatically. 

Alpha handling is contingent on the plug-ins taking care of this. If they don't, like I would imagine certain OpenGL-based effects don't do in Boris FX due to limiations of the process and how they work in general, then there is little you can do about it. Still, that would be kind of odd, all things considered. So start by exploring whether you've not missed some specific settings in the effect itself. Other than that of course there may be ways to create an Alpha channel after the fact using channel operations, but that depends on what type of effects you actually use. Dark particles on colored backgrounds may require different procedures like glowy effects on black...

Mylenium