^ Yes, stuck on high speed is most common, but it also depends on which part of the resistor module failed. The most common is the thermal fuse, which would cut off all speeds going through it (and usually full speed still works because it bypasses that module) but as a vehicle ages, individual resistive elments in the module could develop high resistance and fail to perform as they should, too.
Either way, replacing the blower motor does not necessitate replacing the speed controller. There is no penalty to wait and see.
Either way, replacing the blower motor does not necessitate replacing the speed controller. There is no penalty to wait and see.