Oh yes, they will get bored! They do sleep a lot to conserve energy for hunting, but They would do a certain amount of prowling and hunting during the day. This is why cat behaviorists recommend environmental enrichment for cats, especially in shelters. Rotate toys; put some away and bring out others the cat hasn't seen for a while. A small simple fish tank or a bird feeder outside a good viewing window gives them something to watch. Hiding dry food around the house or in puzzle toys allows them to have something to hunt. This breaks up the monotony of their day. Otherwise they will sleep too much (and want to keep you up all night) or they will eat out of boredom and end up fat.
