Can the PulseInOut module handle quadrature encoder signal?

I am planning to use a rover 5 platform and its motor controller from
https://www.sparkfun.com/products/11593

There is on-board encoder mixing circuit and I wonder if the PulseInOut module can handle it, If yes a small example of how to use this module is more than appreciated. If not then how can I handle 4 quadrature inputs from a board like Cobra II and have some processor time for the other logic.

Not without you rewriting the code that goes on the little micro but we have this https://www.ghielectronics.com/catalog/product/465 and https://www.ghielectronics.com/catalog/product/457

@ Gus - Ok so to use this https://www.ghielectronics.com/catalog/product/465 with 4 encoders I need four sockets for 4 modules and about $92.
Is there any other option that don’t waste sockets or money, also note that I need only one channel for each encoder as the sparkFun board already do the mixing.