The answer is yes. Since trypanosomes do not enter cells, they are well exposed to antibodies of the immunity. They are not fully eradicated by the immune attack due to antigenic variations that enable some of its population to be unrecognized by antibodies. Keeping their surface antigen static would, therefore, improve eradication of Trypanosomiasis
The drug would be administered after infection. This is because the drug most likely works against the genes and metabolic/biological pathways of the trypanosomes responsible for their surface antigens. This would allow the immune system to easily form antibodies against the surface antigens. There would be no fear that the trypanosomes could vary their antigens hence evade the immune system.