No!
When traveling you can and often do use a passenger seat. Many pilots commute to work or back home after their flights. The commutes can be crazy. There was a fellow I knew who lived in Zurich and worked in Guam. You’ll see these men and women in the cabin wearing their uniforms. They travel “space available” which means the airline will board everyone who has a ticket and if there are any remaining seats, they’ll distribute them among those wanting to travel.
One of the great things about being a pilot is the ability to use the cockpit jumpseat for personal travel. Since there are very few employee groups who are allowed in the cockpit, it’s often open.
Some jumpseats are very nice and comfortable.
Others are very uncomfortable
Lastly, there are some airplanes that have a small bunkroom that is used by pilots on very long routes with multiple crews. If a pilot happens across that kind of airplane on a short flight, the crew can let you use the seat in that area for travel.