An airline can base its crews at any down-route station to operate distant sectors on flights originating from the home country, as BA did at Sydney for a while. An airline can also have bases for cabin crew at any destination (subject to political agreement) as some US airlines do in London, and Virgin has in Nigeria, China, Hong Kong and Japan. These are 'local employment' deals, which are entered into, at least in part, to grease the political wheels.
Basing aircraft in a foreign country is a quite different proposition, and runs into all kinds of regulatory obstacles which, in effect, make it impossible. To all intents and purposes, what you are proposing is that Virgin starts an Orlando-based airline using G-registered aircraft and JAA-licenced crews. The proverbial snowball's chance in hell springs to mind...!
Virgin is having enough difficulty leaping all the hurdles to establishing a bona-fide US airline; it would not waste its time trying to sneak a quasi-airline past the FAA!