If you ask me, putting the site online is really a good idea as client can experiment with all the features etc and can let you know very quickly if there is any problem or you are going in the wrong direction
It can become a headache sometimes when you say cannot work for two days and the client sees that nothing has changed in the cart, he might conclude that you are being slow in work etc
Finally, It all depends on your relationship with him, but I will always go with online shop



