Always nice to see a bit of Alternative Reality!! As a kid I painted my Airfix Concorde in RAF bomber colours (albeit purple and green).
On initial view, Concorde does have some apparent advantages as a mil aircraft - the ability to sustain Mach 2 for a considerable period being one of them.
By the time Concorde was being produced, high flying supersonic bomb or missile carriers had been replaced in the Strategists plans by low flying, camouflaged ones. (In some ways you could compare it with the XB-70)
I always understood that Concord had to be predominantly white to avoid heating effect at sustained Mach 2 flight. IIRC Air France couldn't fly the 'Pepsi' aircraft supersonic for that reason.
The aerodynamists would no doubt be able to give you their opinion on the undercarraige of weapons and lack of folding pointy nose on the 'bomber' illustration as well.
As a fast transport it may have been more of a success - the Comets of 216 were just about ready for replacement - but the limited carraige and limited door size would have been a problem. That withdrawing from East of Suez. oh, and the equipment arriving three days later by C-130!
In fact the only realistic military use for Concorde (other than a fast target and research airframe) that I could see would be as a VIP transport, as much for the kudos factor - following Press, bags etc would have to be in another Concorde or good ole VC-10