* How bad is the pump? A pump that's barely functioning might cause gradual damage over time, while a completely failed pump will quickly starve the engine of oil.
* How quickly is the problem addressed? If the problem is caught early, the damage might be minimal. Driving with a failing oil pump for an extended period greatly increases the risk of severe damage.
* Engine design and tolerances. Some engines are more sensitive to low oil pressure than others.
In short, a bad oil pump is a very serious problem that significantly increases the risk of engine failure. It won't *automatically* blow the engine, but the consequences of ignoring it are severe. If you suspect your oil pump is failing, get it checked by a mechanic immediately.