!!! Working in Bryce 5.5c !!!! I have not tried this with other versions.

I took an image, Paulsjs75's cat head. copy and saved it as a .bmp, .png, and .jpg. These file types are un-compressed, lossless-compressed, and lossy-compressed.
In a new instance of bryce I created a sphere of default grey material. I then changed the diffuse channel to an image texture and loaded one of the image types. The second image space was cleared to white. I entered the material library, saved the material and then exported it. Here's the file size comparison:

original image size: :exported Bryce mat file bmp 9.00Mb 5.19Mb png 2.87Mb 6.25Mb jpg 893kb 5.25mb
I also did a difference check between a copy'd extraction from each mat and the original file that produced it. There was none.
So Bryce does compress, losslessly.

I repeated this with a solid black image. original image size: :exported Bryce mat file bmp 780kb 2.15kb jpg 4.86kb 37.8kb So Bryce compresses images losslessly.

Why the file size explosion AS describes? I'm not completely sure. (But I have an idea.)

Let's try AgentSmith's experiment, I'll ccp it here so you don't need to link. Take a blank bryce scene, put a sphere in it and save the scene. That .br5 scene file should equal about 251kb.
Now I'll apply a 1024x1024, 200kb .jpg to that sphere, and re-save the scene. It won't equal 451kb...in fact, it equals about 2,682kb (2.6Mb)
You will get about the same .br5 file size if you use (import) a .jpg versus a .bmp/.tif/etc.

AS

I did this, I'm going to use the same 9Mb cat head picture from before. Because it's big, so the difference should be obvious.
Sphere with matte grey material= 122kb.
Sphere with 9Mb image material= 5.29Mb.

Go figure. Maybe it's just my Bryce that does it.