What type of controller? Off hand I would say yes, but that would be overkill. High speed counters are usually used for rapid transitions such as parts counting, inputs from encoders etc. A push button would normally feed a standard input.
You can count the number of preses of a buton with a high speed counter, but an ordinaray counter will allso do.
Also tell us wich PLC you are useing as R_stone said. It'll help
You have to be very careful using a high speed counter input with a pushbutton or any mechinical switch because of contact bounce. You end up with more than one count per button press.