Scott,
Yes, it will grow back with a vengence next year!
I would build it a nice trellis to climb on. Or if you can afford it, buy a good strong trellis, it is strong.
It would look really nice on a trellis in front of the fence, you would have to buy that green "tape" they sell to train it where to grow tho.
Next spring look for the tape and build it a nice BIG trellis.
You are fortunate to have such a nice big vine to cover the fance next year.
Whatever you do, don't fertilzie it. It won't bloom.

Thanks! That's a relief. I have another question: will the thicker branches that have been cut actually grow again from where it was cut or will they just new shoots of them?

No, the thicker stems that have been cut will not regrow. But they will very likely generate some new shoots along their length. Given some time, these and other small stems will get some heft to them just like the ones cut - eventually even larger. Mature wisteria vines can develop trunk-like stems a foot or more around

And using the term "trellis" with a wisteria is misleading. You will need something much more substantial than a simple wooden or metal trellis to support this vine. wisteria vines by twisting their stems around the support structure and that torque can be very powerful. I've seen wisteria pull out 3" diameter metal posts (like the kind they used to use for clotheslines) and take down an entire deck. Typically, the recommendation is that what ever structure you devise for a support, it should be anchored by at least 4"x4" timbers set in concrete. Something like this is more appropriate but you don't necessarily need that much depth:

And keep it off the fence itself.

Also, fertilizing wisteria will not prevent it from blooming. You just need to be careful about the type of fertilizer - one with too much nitrogen (like lawn fertilizers) will encourage leaf production over flowering.

Thanks for the information. I have seen the one in Kew Gardens London a couple of times. They made a very large steel support for it in which you can walk inside of, it's grown 15' plus feet high and 10' feet round. It's absolutely amazing. I've heard and seen (mine) vine grow 60' long. It has also appeared to strangle my chain link fence.