As Dutch Roll in the 707 and 727 were tricky to handle without a yaw damper, the 737 prototypes were originally fitted with two YDs due to anticipated MEL restrictions. Once they flew it, it was proven to be a pussycat and the second YD was removed. There is also no MEL restriction if the YD is inop.
In my experience in both 737 Classics and NGs if you induce a Dutch Roll at cruise alt & Mach it will decay to zero in about 6-8 oscillations with the YD off, or just 1.5 with the YD on - both figures are without any pilot input.
S&L