Parts can be welded prior to anodizing. The use of 5356 welded rod is strongly recommended, though some discoloration will still occur. 4043 is the worst choice because it will turn a sooty black when anodized.
Grinding away the weld before anodizing will result in decreased mechanical integrity and will not solve the problem of variations in appearance.
It is not a good idea to weld after anodizing. Because most welding processes require electrical conductivity, the anodic coating must be ground away where the weld will be applied. This normally results in an unsightly mess around the welding area.