If this is the bent rod you speak of, you will indeed have sync issues.
the needle plate may also be bent, especially if someone tried to open the throttle while the throttle valves were varnished/stuck.
The red arrow points to the needle plate. The plate keeps a pre load on the spring. If the plate is bent upward, (spread apart) the spring is no longer effective, and throttle rod looseness results,
and the carb will never sync correctly. If you take it apart, it'll make sense. If you suspect this scenario, compare it to one from another carb. BE CAREFUL if you do, those plate mounting screws are very prone to stripping out. Hopefully the phillips heads aren't too rusty.