That's in the by-laws, which I don't have access to. But, generally speaking, the answer in the NHL is: no, they cannot be "traded".
Now, that's a technical read. The process, AIUI, is a person (say coach Randy Carlyle) can leave for a new (usually better) job with another organization. If such a person is still contracted to the organization, they can work out a compensation for allowing the person to break his/her contract. The Ducks surrendered a 2nd round pick a few years back to get Randy Carlyle as their coach. I thought Ron Hextall leaving Philadelphia for Los Angeles (Asst. GM) also garnered a 2nd, but I could be misremembering.