no - it wont, the pump makes noise in two most common circumstances.
1 - the pump is internally damaged and cannot generate pressure
2 - the oil is aerated.
in your case no.1 is most probable, the 2nd point usually does not apply to toyota as they are very good in self bleeding air out of the system.
and because the pump has damaged itself, it has dispersed metal into the steering system - and as there is no proper filter in the steering setup, it is advised to completely flush out the steering components, it is done by disconnecting the return line and manually working the steering with engine off.
make sure all return line connection clamps are tight and solid, if you see seepage at any joint replace that clamp, it will let air into the steering and cause pump noise and low assist.
