Not at all.
I've cut them all the way down to about 12" from the base and the banana came back like nothing ever happened.
Here's how tough these bananas are.
I wanted to do some renovation to one of the beds where I had a clump at and I took a saw to the bananas and leveled them to the ground, took a shovel to the clump and then tossed a couple of them into the compost bin and buried a couple of the other ones just to get rid of it.
About 2 months later I had sprouts coming out of every one of the plants I butchered.
