@cwal This question is very interesting, but I had never thought about it before, so I did some research. What I learned was possibly.

Factors that infer more likely failure to convert to negative include cavitary infection vs nodular, low body mass, and poor nutrition. Lower on the list were extensive infection (large parts of lungs involved) and positive AFB smears (usually indicates presence of more bacteria. )

Positive outcomes increase when the 3 antibiotic regimen is followed, and continues for 12 months after conversion to negative.

There is a lot to read on the subject, I am limited in posting links by being on my phone for this week.
Sue