Unfortunately aerender (the command line renderer that BG Renderer uses) does not have access to the GPU. Btw multi-processing in After Effects does not either since it also uses aerender. If you would like Adobe to add GPU access to aerender please request it from them here: http://adobe.com/go/wish
Does the background render script not use the GPU for rendering 3d created inside of AE? Normally every render I do is with the background render script to image sequences, then it goes into AME if I'm rendering out video for a server or into Vegas if I'm going to mix. With my z620 with dual 6core Xeon's I can usually get 10 different renders going of the same comp if it isn't GPU or too CPU intensive.
Today I had a 3D rotating cube in a comp and I did one background render then started the regular
render que and After Effects rendered between 5-8 frames for each of the one that the background render did.