The short answer is yes, it could.
This PDF file, citing Chapter 16 of a Military Dermatology textbook,
titled, 'ATYPICAL MYCOBACTERIAL DISEASES', notes the following:
"M szulgai, first recognized in 1972, is a rare pathogen
with fewer than 20 total cases reported - of
which most have been chronic pulmonary disease
in middle-aged men with fewer than 6 cases involving
skin or soft tissue. Apparently, this organism
is distributed worldwide with no known natural
The above paragraph suggests that this pathogen could be contracted
almost anywhere in the world.
More to the point of its presence in Vietnam:
"Although atypical mycobacterial infections per
se are not mentioned in Lieutenant Colonel Alfred
M. Allen?s landmark volume on dermatology in the
U.S. Army, Skin Diseases in Vietnam, 1965-72,
several reports of that era record infections with these
organisms. In a report published in 1963, 12 orthopedic
cases were discussed, with atypical mycobacterial
infections of tendon sheaths in one half of the
patients and involvement of joints in the other half.
Three of the tendon infections followed laceration or
hydrocortisone injections, and three of the six joint
infections followed repeated injections of hydrocortisone
into the affected joint. The exact atypical mycobacteria
species in these cases were not identified,
but M ulcerans and M marinum were ruled out
by bacteriological studies; thus, given the culture
growth characteristics, the offending organisms
were most likely M fortuitum, M kansasii, or M szulgai."
A later paragraph explains the relative rarity of these
types of infections in Vietnam, and suggests a possible
"Another report described M fortuitum infections in
three severely wounded Vietnam veterans with deep
soft tissue abscesses; all eventually healed following
extensive debridement, incision and drainage, and
local wound care. These three cases were the only
ones found among the large number of injured
patients returning from Vietnam and treated at
Valley Forge (Pennsylvania) General Hospital. The
low number of cases may have been attributed to
the aeromedical evacuation system that was used
during the Vietnam conflict, which rapidly removed
the accessible wounded from the battlefield, thus
preventing continued contact of open wounds with
water or soil contaminated with atypical mycobacteria.
Rapid removal of patients with extensive
open wounds to relatively sophisticated treatment
facilities with good laboratory capabilities is essential
in minimizing delays in diagnosis and effective
treatment of atypical mycobacterial infections."
If you were not fortunate enough to have been among those
who received rapid evacuation via helicopter, this would
have increased your chances for exposure and infection.
All of this, and more, from this PDF file, already noted:
Additional information may be found from further exploration
of the links provided above, as well as those resulting from
the Google searches outlined below.
Searches done, via Google:
"mycobacterium szulgai" vietnam
"m szulgai" vietnam