No. No, it won't affect the program at all.
The ones killed are the (somewhat, not quite-innocent) ignorant laborers and soldiers and their guards and officers digging the tunnel in the radioactive dirt and rock. They can be replaced within hours by more starving, ignorant, soldiers and slaves.
The generals, the “scientists” and - most especially - the government leaders directing the project were nowhere near the tunnel site. Obviously, we might have gotten lucky and somebody was touring the dig site in the tunnel. But so you really think the leaders would go underground into the radioactivity, dirt, and discomfort just to look around?
Assuming the number of rescuer's that died is reported as true, there had to have been a least a few senior level military involved in the initial collapse. Probably conducting inspections.