Yes, disengage all,locks, including the legs, which can be locked just enough to hold them in place. This applies to storing a tripod, never leave the locks tight, just loose or slightly set, so if forced they will slip instead of breaking.
Large Video/Cine tripods and heads, are normally placed in separate purpose built boxes, Anvil made some lovely custom Vidoe Head cases, that weighed as much as the Video Head. Studios use these, box the sticks in one case, or hard tube normally, and the heads are removed from the sticks, and placed in its hard shipping case. This is the best way to transport a good tripod/head setup.
When shipping, I would recommend either double boxing with lots of bubble wrap, or a purpose build tripod tube/case. I have shipped tripods in these cases without issue. But just shipped a small tripod I had a shipping company pack, single box, and it arrived damaged. So, going back to tripod hard cases (not the soft bag type, which are only good for local transportation, like in your car).
Cheers