It will also depend on the grade of alloy used for the pulley in the first place – so the properties of this are unknown, but might be an appropriately econonical type for casting, without necessarily a great concern about welding qualities.
however, I would suggest that a pulley in normal use is not a highly stressed item, and it may not matter if the tensile strength is somewhat (even substantially) down.
I would be concerned if the item was in heavy use in an industrial environment, in which case the recommended replacement should be purchased from the original manufacturer. For the amateur workshop in light use, one not be too worried – if a welded inserted piece seems to be fully and evenly bonded, that is good enough.
Martin