You need to "notionally" do network access to get these data for images. But the images might come from the browser's cache if they're already available. You can encourage or enforce caching through a combination of web server headers and a cache-manifest file. Or you can just preload your images when your game starts so they're already available.
Once you have an Image object in memory, and you're holding a reference to it, it's not going to go away and you can use it without a problem. But when a player comes back to play the game again (in the same browser session or a different one), the assets need to come either from the server or the browser cache.