Pontius
you assume the Indian Army would continue fighting for the British after the Germans had motored through the Middle East - I think that's a big assumtion TBH. The collapse of British arms in the ME would probably have led to a de facto collapse of the Raj and a takeover by Congress.
Apart from our losses the supply chain would have been unsustainable and, at the end of the day, the UK Govt would want to hold onto the Britsih Isles even if it meant the abandonment of the Empire....