Absolutely feasible - it depends on the standard you shoot to though! You may be aware that .22LR is very ammunition sensitive, and Tenex is by no means the best available for every barrel. A better matched box of Club, SK etc may well group better than a less suitable box of Tenex.
In short, have a go with the club's ammo. If it will hold a group that you are happy with then go with it, but it's worth trying something else every now and again to make sure the ammo isn't limiting you.
Dom.