Yes you can use the championship practice areas, remember you are a member
. Pitching is frowned upon unless the shot remains below knee height on most greens. I am not sure what is 'up your end' if you needed to hit a higher pitch.
Ones I use that have chipping areas separate from putting green and allow higher shots (there may be others):
Bonifay (best for a variety IMO), Cane, Evans Prarie and Lopez
Lopez is not at the club house, it is at the gate where you enter the village of Chatham.