Yes, you can overwinter in a sun room. Look out for pests. It's solanacae, tomato/so will attract the same bugs tomatoes and peppers do.
It has to make a fork int he trunk to bloom, if you have a trunk cutting, could take longer, feed it tomato fertilizer. The blooms will knock your socks off! Worth the wait, believe me :)

keep it on the dry side over the winter, it will probably lose some of it's leaves, don't worry about that.
In the spring move it outside as soon as you can, if possible sink the pots in the ground or even plant it in the ground.
Mine bloom best after it rains, no matter what else I do, that is what makes them happy. I give mine fish emulsion and pile seaweed around them (but I live by the beach so seaweed is easy to get). They like a lot of fertilizer and food.
what zone are you? 6a, ah, you can put it in full sun.
Mine live in the ground year round and the only time I have lost one was when we had hurricane Ike, and 4' of salt water in the yard for over 24 hours. They have been through snow, freezing rain, sleet and hail and no casualties. They are tougher than people think.
Good luck.
Tally HO!