I use a controller of position proportional type from the UTAdvanced series with adjusted valve positions. If I download the parameter settings file using the LL50A to modify the parameter settings, will I need to readjust the valve position?

No, simply downloading the parameter data does not require valve readjustment.
However, if the parameter settings of the main unit are initialized, or the initialization command is sent from the LL50A, the position adjustment information is lost, so you would need to readjust the position in that case.