As long as you take proper care of the poinsettias plants then yes you can keep them all year round although some people just keep them for winter or the holiday season.
But some people are able to keep the poinsettias all year round which a bit more care.
The poinsettias will do best all year round when you keep them near some sunlight or use some grow lights to allow them to get enough light and gently remove the plant from its container, soak it well and place it back in the pot to prevent it from sitting in water.