This depends on the texture format. Yes, tga can be compressed (I use GIMP as well). And you could also use DDS. DDS DXT1 as an example can even compress TGA files to about 25 percent of original size. And a game can transfer it in this compressed small size to the GPU. The GPU will decompress it with the S3T algorithms.

But as you can see: All this could be tested when you try to work with real textures instead of untextured place holders. And it can be a waste of time when you have to rework each texture and model just to reduce number of draw calls or to reduce data transfer to the GPU, or memory usage.