When a page is loaded from an AppCache, even when online, external resources such as images will not be loaded at all. If foo.com has an image <img src="http://bar.com/img.png" />, then according to the steps in http://www.whatwg.org/specs/web-apps/current-work/multipage/offline.html#changesToNetworkingModel it will fail the load for the resource. For example, someone with an Offline Gmail client would never be able to see cross-domain images in emails, even when completely online.
There's no workaround in the current spec. For user-defined img tags, like those in webmail apps, the set of external domains is practically infinite. The NETWORK namespace, which requires a known domain for the domain-matching check, won't help. The FALLBACK namespace has to have a known domain, that has to be the same as the manifest's domain, so it also can't help.