Being physically fit will help a lot. The reason is that you need strength in your abdominal muscles, otherwise your throat will squeeze up trying to compensate for it.
Apart from that general rule, I don't know if jogging in particular will help.
proof: there are many fat people with good vocals, do they jog at all? (no offence to fat people, i believe fat & blind people sing better than the rest- my sincere observation this one).
fat ppl has more airspace? i'd know, for obvious reasons..
but you know, i know fat people who are healthier than skinnies, so just to bring it back to topic that it's on overall health and not mass / fat / size / shape etc.. i think blind ppl depend on their hearing alot too so their hearing's refined and specific to pitch.. that's prob one reason why they're better singers,..