Can caffeine be extracted by the body when digesting coffee grounds? I'm told my great-grandmother used to drink the coffee, then eat the grounds with some sugar. Assuming there was caffeine left in them, is the body able to extract caffeine from coffee grounds by digesting them, versus getting it boiled out in the form of coffee?

Or in other words, if someone were to eat the grounds without drinking the coffee, could he feel some caffeine effects?
Yes. Coffee grounds are simply the ground up seeds found inside the berry of the coffea plant, so eat up! Even after the beans have been ground and extracted into your favorite coffee beverage, they still contain plenty of caffeine and are perfectly digestible. 

Before people learned to brew coffee, folks were eating the beans to get that coffee boost. Today we eat straight coffee beans through all sorts of preparations. Chocolate covered espresso beans are quite popular and pack quite the kick.

Eating coffee beans has even more effect than drinking coffee because not all of the caffeine is extracted through your brewing process. According to the Journal of Agriculture and Food Chemistry, leftover coffee grounds from filter and espresso-type coffeemakers are especially abundant in antioxidants. Plus, you'll get all the benefit of the dietary fiber that's not present in your morning brew.  Enjoy!