We had it in the flat we just sold. It depends how close to the property it is as to how much it will put off lenders/buyers. A treatment/management plan is technically all you need.
The chemical treatment doesn't actually kill it, it just suppresses it. If you disturb the roots, it will spring back into life again.
The treatment is pretty effective though, ours disappeared and never came back and the treatment came with a 10 year guarantee. You can get rid of it totally, but they have to dig a big fuck off hole to make sure they get every last bit of it. If it is coming in from adjoining land, that's probably impossible.
Even according to the guy who did ours (CYB Environmental - highly recommended), there are far worse plants for structural damage (some climbing roses, for example) but JKW was jumped on by the lenders at the time of the 2008 crash as an easy reason not to lend. Unless it's already coming up through the brickwork, there is pretty much zero chance of it giving you physical grief if there is a management plan in place.
For me personally, I wouldn't go near it, just for the amount of stress it causes at remortgage and sell time. We probably lost half of our interested buyers when they heard about it. First offer we accepted was over asking but they pulled out when their (fucking moron) mortgage advisor told them banks wouldn't lend. Still sold for asking price eventually, but fucked if I'm putting myself through that again.