Is there an easy way to make covers backgrounds that are more textured and softer in tone than the default color swatches? My art looks great, but the backgrounds could use a little work. Is it possible, for example, to put fabric in my scanner and then apply that as a background?

You could certainly scan fabric (or cardboard, or paper, or...).

but why not play around with texture filters? There's a TON of ways to run filters (effects) over a solid color layer (i.e. behind the main artwork layer(s)) to simulate everything from dust and speckles to craquelure and tiles. Open a new image (200 x 200--no need to kill your CPU) in GIMP or Photoshop and Select All and start playing with the texturing filters and effects. Randomly splatter on some small black dots and play with embossing effects.

The sky's the limit, when it comes to texture play. There's whole articles written on Gamasutra about how to make textures (and texture tiles), from photos to digitization  to special plug-ins (mainly to proper tile a texture that is too small for the area being covered).

And there's always just searching stock art galleries (or even Google images) for textures that tile well, to apply to a layer (probably with the Fill tool or by using the texture as a brush).

Hope this helps to get you started on your research and play;
David