Apparently not. Ivy isn't parasitic so doesn't take any nutrients from tree trunks. It is also a wildlife haven for insects.

the only way it might eventually kill it is if it gets right up into the canopy and completely covers it, choking out light and air from any walnut leaves which try to grow, so I suggest you keep it down by cutting off excess growth.

if the branches get heavily 'loaded' the weight may cause branches to snap off in strong winds. If its a concern just trim it back.

Yes agree with bamboo, if left it will take over the whole of the canopy, you need to cut it off near to the base, however please note that if it is quite thick round the trunk then certain birds may be nesting in there, ig, wrens,tits, dunnocks etc, so if this course of action is needed then wait for the nesting period to be over.

I agree with Cammomile. If it's a fully grown big tree then the Ivy poses no threat at all & it is a shame to cut it at the base & completely get rid of it. It is a great haven for wild life as others have pointed out, so just trim it a bit if necessary to stop it from getting too much at the top.