Search and rescue dogs do their jobs despite travel stress. When disaster strikes, you want the very best tools, functioning at their peak. In the case of catastrophic earthquakes, tornadoes, or even bombings in war zones, those tools are search and rescue dogs. But researchers have found that getting dogs to disaster sites can add to the animals' stress. Source 2x.
I think that dogs that are trained to do search and rescue can be stressed just as much as their handler. Just as a short flight or a long flight can at times stress others can handle the flights with no stress. These dogs do a great job and I think that allowing them a couple hours of down time once they get to a site can help the stress too.