Generally, no.

In Jain Dharma, a Jain monk (sādhu/muni) is one who follows very strict vows of ahiṁsā, aparigraha, and restraint. Using vehicles or flights is not in the normal conduct of a Jain monk, because it involves movement, attachment to comfort, and often increases violence toward living beings.

So, a person who regularly uses cars, trains, or airplanes would not ordinarily be called a Jain monk.

There may be rare exceptions in some traditions for necessity, illness, or specific circumstances, but as a rule, monastic conduct in Jainism does not include travel by vehicle or flight.

If you want, I can also explain the difference between a Jain monk and a Jain follower (श्रावक/श्राविका).