Yes, as long as watered regularly and is kept in warm temperatures.
You can make a tomato plant thrive indoors and even produce fruit if you assist in the pollination of the flowers with a very small paint brush. A friend has a tomato plant in his kitchen that is 3 years old and still bears fruit. It will require you to add fertilizer to the water supply. If you water with tap water, let the water sit or breathe for at least 24 hours to allow the chlorine content to evaporate before using it to water your plants. If not, the chlorine can kill or severely weaken the plant. The plant must be an indeterminate variety. This means that the tomato will continue to grow till it is killed. Determinate varieties will grow only for one growing season, then stop producing fruit.