I don't see that jet washing will cause any damage but I'd have a word with them first. You shouldn't do anything to a neighbour's fence without permission.
You should really tell your neighbour what you plan on doing, if only to preserve good neighbourly relations. If you just go ahead with jet washing, and don't mention it beforehand, your neighbour might get the impression that you don't care what he thinks. And, as chas2008 says, somebody might just be standing on the other side, watering their plants.