Yes, this IC will work. But you will not see a difference at all, since the clock sent to the Z80 is the same.
This 6 MHz is very common and quite cheap.
To get a real speed improvement you will need the 8 MHz Z80 and change the clock.
See
this page for socalled 7 Mhz clock circuits, the Superturbo circuit is made up of standard components and easy to assemble.