I grow tomatoes in my greenhouse all summer long. I use 5 gallon pails and they are indeterminate cherry tomatoes that grow to the ceiling and along the rafters (although I'm going to change from that because it's hard to reach the ripe tomatoes way up on the roof like that!
) I also grow the bush type in reds and yellows in the same 5 gallon pails. I use water crystals mixed into the soil to help me keep them properly watered as they grow larger and demand more.
I think you can grow them in any container BUT you have to be sure they are well watered.......could you keep them properly watered in the hanging basket you're planning to use? It might be fun to grow the cherry tomatoes and have them cascade down but I think you'd have to watch what kind your buying as most tomatoes would not cascade nicely for a hanging basket.
Always fun to try something different and what do you lose if it doesn't go well. I'd be watering more than once a day in the heat of summer as the fruits are developing if I were using a hanging basket.