My (admittedly limited) understanding of how vaccines work would not lead me to expect any direct link between drug-resistance on the one hand and vaccine effectiveness on the other. Consequently, the TB vaccine should be as effective against these strains as against more common variants of the bacteria. Both the US CDC and the WHO have fact sheets on the disease that state as much, while suggesting that conclusive evidence is not available at this time and that vaccines aren't generally that effective for adults.
From the CDC:
The TB vaccine is called Bacille Calmette-Guérin (BCG), and it is used in many countries to prevent severe forms of TB in children. However, BCG is not generally recommended in the United States because it has limited effectiveness for preventing the most common forms of TB and in preventing TB in adults. The effect of BCG against XDR TB would likely be similar to the effect on drug-susceptible TB.
From the WHO:
The BCG vaccine prevents severe forms of TB in children, such as TB meningitis, but is less effective in preventing pulmonary TB in adults, the commonest and most infectious form of TB. It is expected that the effectiveness of BCG against XDR-TB is similar as for ordinary TB. Nevertheless, new vaccines are urgently needed, and WHO is actively advocating for the development of new vaccines.
Bottom line, being vaccinated might not be enough to be completely safe against TB (whether drug susceptible or not) but the vaccine does probably afford the same level of protection against MDR or XDR TB.
Also note that while it's a significant public health problem, drug resistant strains are still relatively rare. Both the CDC and WHO fact sheets touch upon travel and do not advise against going to countries where cases have been reported, unless you are also HIV-positive. Instead, the CDC recommends avoiding “high-risk settings” like “crowded hospitals, prisons, homeless shelters”.
Incidentally, I am not sure Africa is a hotspot for MDR or XDR-TB (as opposed to tuberculosis in general). MDR mostly develops in patients who have been treated for TB before and Wikipedia indicates that
About 60% of these cases occurred in Brazil, China, India, the Russian Federation and South Africa alone.
Outside of South Africa, Africa's problems are different, it's simply regular TB and the lack of access to even basic healthcare for many people. OTOH, if people do not receive treatment and a country has no capacity to test for drug-resistance, the problem could also exist for a long time without being reported.