It would be highly, highly implausible (note that even the YF-12 got farther off the ground- pardon the pun), but I could easily see perhaps two or three examples existing (YB-71) for a testing phase in much the same way as the YF-12s.
The armament would be highly limited- perhaps two to four weapons, probably missiles that would need to be specifically designed for the plane, so cost effectiveness would be incredibly low compared to the workhorse B-52s, B-58s, B-47s, and the planned B-70s, which could carry much heavier loads (and in the case of the B-70, at nearly the same speed). A B-71 would be very much a one-shot weapon- fire, go home, reload- that I doubt the USAF would commit to it when the already had the B-52s with long standoff ranges, the B-58s, FB-111s, and plans for B-70s with high speeds and much larger payloads- and on the other side, large numbers of ICBMs.
A B-71 would be somewhere between a bomber trying to be an ICBM and an ICBM trying to act like a bomber.
So sure, it's possible SAC would buy it- they had a practically unlimited budget at that point- but it's just not likely.
That said, if they did buy it, it probably wouldn't be used outside of World War Three. It's far too costly to use the thing for, say, the Gulf War- it costs a lot of money to fly the bloody things, and they don't carry much weight- a B-52 can put many times more weaponry on targets, dollar for dollar.
The YF-12 was a good idea- a very high-speed interceptor makes sense. The SR-71 was a good idea- a high-speed photorecon plane makes sense. The B-71 isn't a great idea- a high-speed bomber that only carries a couple of bombs doesn't make much sense when you've got ICBMs and plans for B-70s (which are high-speed bombers that carry quite a few bombs).