Undoubtedly. I believe there are about two dozen white-tops assigned to HMX-1 for HOS transport, both VH-3s and VH-60s, along with the other support machines. And then there are the USAF resources, which are entirely separate. The U.S. President's logistical tail must be seen to be believed.
Whether the machine is stuffed in a freighter or ferried under its own power probably depends upon a number of factors like overall distance traveled, availability of other airframes and other near-simultaneous transport requirements.
Cost is probably way down the list for both.