I'm trying to be sure that I understand correctly.
Thanks.
Where it's saved [on your own computer] shouldn't really matter as long as it finds the path to the texture file... but if you're wanting to share the file with someone else, probably is best to pack it so that it will be able to find it.
I can load and pack an image for the main texture, and apply it to the GP material.
I can't find a way to use a packed image as a preview/thumbnail. (Screen capture didn't work for me either).
Maybe this is good enough, or maybe it isn't worth the trouble.
Update: It seems that loading a custom preview image for a material asset automatically packs it into the blend file. I couldn't find this described in the documentation. [I drilled down into the Data API and it looks like the pixels are defined in there.]
If you want the "main" texture packed into the .blend file, the image must be packed manually before assigning it to a material.
[Also, a second try at screen capture (from the asset browser window itself) was successful. I guess there is more to this operation than I am understanding.]