I may have misunderstood you. If you plan to download and save images to a user’s hard drive, you can’t. There is no write access to a user’s hard drive from webgl.
If you download images, you can apply them as textures or sprites just like normal, they will just sit in memory. These are not compressed by the project. (this is with www)
If you asset bundle them, then compression can apply. These can be cached, but I believe most web browsers have a limit on cache size, which is also cleared when the browser is closed (not sure if the second part is true for normal mode, but private mode or the user can clear it pretty easy).
Now, if by download, you mean download and include them in the project, nothing wrong with that. It’s just a normal image file and you can crunch or compress or whatever you want to it.