It's been a while, but the 727 has issues between lateral (high) and longitudinal (low) stability. Don't think the T tail has much, if anything to do with it, though get too much yaw (11° is the magic number in the back of my head) and the tail will reputedly come off.
The 727-100 will depart if Dutch Roll is left unchecked (you'd have to be dead not to notice it), though the 727-200 is pretty-much neutral (longer, and more directional stability), but obvious i.e. it won't recover itself, but won't get worse.
18-Wheeler is correct: initial actions include extending the speedbrakes - very effective - lessens the lateral stability. Hand flying the recovery (the only way) is difficult, especially in the -100, as it's easy to get out of phase with the roll and make it worse. The recover is ideally a 2-person job with the other guy checking to see that you have the correct inputs - mostly an input timing issue.
The aircraft has significant MEL restrictions relating deispatch with inop yaw dampers.