it depends on the game, some need a network connection, some don't, some will have limited functionality. You can try it by just turning the wifi on the tablet/phone off and checking the game to see if it works or not.
Thanks for posting, I realised after posting that I could switch off wifi and it seems they do work. Now just have to fathom how to set the security so that my dd does not inadvertently buy anything as it seems very easy too Not that I have btw!
Instructions on that here - depending on what version of Android you are running, you might need to scroll about half way down the page to the section on restricting in-app purchases.
If you want to stop her being able to buy anything at all, don't add a card to your play account, use the gift cards instead so it works on a pre-pay basis and once the balance is spent, you can't buy anything.