Not really relevant to the topic, but could be helpful. My Garmin 450 has the carabiner clip. I usually have some sort of pack on and I clipped the gps to the adjuster strap on the waist belt and left it on. Helpful to have the track recorded. YMMV.
Do all Garmin units have the capability to leave it on and track record and if so, does doing so significantly reduce the time between battery changes?
It does reduce battery life. The Oregon 550, I carry, has an advertised battery life of about 16 hours. In real world use, I can keep it on all day when I'm hunting and have to charge it at the end of the day. I'd say realistically, I'd get about 10-12 hours of use from the 550. The 450 should have about the same battery life as the 550.