No, I wouldn't try to drill out those screw heads.

Those screws are SUPPOSED to be brass or stainless steel, and if they're badly corroded someone has replaced them with ordinary steel screws, which is why they're stuck.

Those screws screw into the overflow and drain assembly behind the front of the tub, and if you can't get the screws out of the overflow, you'll have to replace that whole assembly. That may mean cutting a hole in the wall behind the tub to get at the assembly from the back or cutting a hole in the ceiling below the tub to get at the assembly from below.

If it were me, I would use a Dremel tool (or any other such tool) to cut the overflow cover off around the screws, and then apply diluted hydrochloric acid to where the screws enter the brass overflow elbow using an eyedropper or Q-Tip. Hopefully the acid will be drawn into the crevice between steel male threads and bronze female threads amd dissolve the rust there so that you can remove those screws.

Keep applying acid and twist the screw heads with a pair of vice grips and hopefully you can get the screws out. Otherwise, replacing that overflow and drain assembly is going to require you get behind the front of the tub or you somehow gain access to that assembly from below.