Lucian said
It's completely plausible in the Falloutverse. As stated above, fully-functioning androids have been made. I assume it'd be even easier to integrate cybernetics into a Ghoul, because of their cellular regeneration factor.
Your statement (easier to integrate cybernetics, I.E. grafting into preexisting wetware) presumes that Androids are initially human. They are not. Androids are, as their name indicates, Robots that have been made to mimic Humans. The term you are searching for is Cyborg - and while cybernetic augmentation is not quite as rare as Androids outside of the Commonwealth, it is notably much less advanced than displayed in your character, and even pre-war standards are not quite up to the task of reproducing your setup. While they had gotten quite good at neural integration - as demonstrated with robobrains and available implants - actually full-blown cybernetics such as integrated plasma weapons were beyond their capabilities. They could manage the lower and higher extremes of the modification spectrum - they could give you minor implants, or they could pull your brain out and stick it in a jar. The more advanced the technology used, the higher the chance you'll wind up disembodied.
Your ghoul is something I might expect to see at Big Mountain, full stop. I don't see any Wasteland Surgeons, the Enclave, The Followers or the Apocalypse, or Vault-Tec experiments producing one. In fact, other than Big Mountain, the only actual faction I see that could have been involved in the creation of such a product would be The Institute. If we are being honest, the equipment - armor, weapons, accessories, the combinition ghoul/cyborg kit - is something I would expect to find in a Min/Max arena character profile. Not in the advanced section.
I'm not the GM, so of course my opinion only carries so much weight: But I would not get your hopes up about being accepted unless you somehow manage to pull together a fabulously cohesive and well-thought backstory, and even then it would be iffy. Other characters here had to make notable concessions for lesser problems than the pile of them your character has.