Yes. It's called "cable stretch," and it's normal, but it really isn't the cables stretching. It's the housing bedding into the housing ends, and those bedding into the housing bosses on the bike. The better job that the shop does on this detail work, the less stretch there is. In any case, learn to adjust your own cables. Have your LBS show you how, both derailleur and brake. It's normal to have to adjust something every couple weeks if you ride much. Can't be fooling with taking the bike to the shop that often! This will happen to some extent every time you recable the bike, which most folks do every year or two if they ride a lot.

No, it's not OK to ride like that, at least not much. Not that you'll really hurt anything, it's just unpleasant not to have the shifters function properly.