Basjoo grows wildly here in Zone 10 (Fla). I avoid that particular breed...
The Basjoo is a fighter, survivor, cold hardy banana what will own your backyard unless properly managed. They 'pup' with a mission. So keep an eye on them.
This forum shows how to properly remove pups...you can sell them on ebay

And yes, they will need feeding....or your garden will suffer.
Richard sells a great fertilizer. I purchase nanna feed from him annually.
Reaction from surrounding veggies may be positive or negitive to the levels of nutrients that are combined for healthy banana growth.
Personally, I would have a seperate 'mat' for the bananas to own. Then you can hit them with a waterhose and throw feed at them without worrying about affecting your veggies if possible.