If the bearings are a bit worn it might benefit from a slightly heavier (high mileage) oil. The oil pump, being a gear pump, isn't going to benefit. The protection comes from the AW additives in the oil primarily, as we are talking about meshing gear teeth, not bearings.
The pump may also not be worn, it could have a leaking pickup assembly, which I know was common with some of the LSx family engines, but I'm not familiar enough with them to know which ones. I believe an o-ring that seals the pickup assembly to the pump gets hard.