I guess I am assuming that there is a difference between jumpseating and deadheading. Jumpseating is "thumbing a ride", deadheading involves crew scheduling. If you are on your own airline, you would most likely be catagorized as a company business travel, and most likely will have a seat assigned. End of hassle. Of course, deadheading in the cabin or the cockpit is up to you and your company.

But assuming that you are jumpseating with another carrier, you had better not be a deadheader without [the company]buying a ticket for you. You may lose your jumpseat privelege with that company, or your company may lose JS priveleges (Great Lakes got spanked with this back in the mid 90's. They were having their guys jumpseat from MSP, DTW and ORD to cover reserve trips, even though they were based somehere else). This is a no-no. They should have gotten them there via their own airline, and if service didn't allow for that, they should have bought a ticket.