I took my type rating check ride in the aircraft, a -100. One of the tests was to recover from an induced Dutch roll. This was a long time ago so I cannot remember the airspeed and altitude where this section of the check ride took place. I think we were at FL 240 and at 300 Kts IAS, I think.
The FAA check airman was in the jump seat behind me and another FAA pilot was in the right seat. The pilot in the right seat turned off both yaw dampers and then induced the Dutch Roll, then just before he gave me control of the aircraft the check airman instructed me not to use the spoilers, but to use the flight controls.
Using the full aileron into the roll stopped the Dutch Roll, the yaw dampers were turned back on and the check ride continued.
I was more nervous about the full dirty stall than the Dutch Roll bit.
As some have said earlier, the 727 was a very nice flying aircraft and when light we used some really short runways, shortest I personally flew into and out of was 4,800 feet. Passenger load was only 15 people and we two hours of fuel on board on takeoff. I was actually more worried about sinking into the ramp/taxiway/runway. Oh, we could use flaps 40, which I did on that runway.
So, also as some one else already posted, to let a Dutch Roll develop into a serious condition, you'd have to be dead already.
And yes, if one or both yaw dampers were out, there were some very restrictive conditions one had to abide by. If I remember correctly, if you lost both in flight, the magic numbers were below FL 240 and 250 Kts IAS. But it has been a while since I flew the 72.