The Big Bad Colors could be ordered with any engine / trans combo. So yes, a 343 4-speed in Big Bad Blue is not only possible but very likely.
Is a complete, running, driving BBB AMX with 80,000 miles needing a resto worth $7,000? Very possible, but without seeing it I don't know. What other options does it have? How bad do you want a BBB? They only made 195 so if you want a BBB they're not easy to find.