Thanks Roff!
I just looked at the data sheets for both and it looks like it could work. It would save a chip and the short counting is not necessarily a requirement since the user will reset the device manually after n number of servos have been actuated. I will see if I have a LS161 laying around. I know I have some LS138's.
One thing I did not mention is the pulse to increment the 4017 counter is from an external device that outputs a 250ms 6v pulse. Every time the user pushes a button on the external device, its output goes high for 250ms. I share the ground between the external device and my circuit.
Thanks!