Even with a thousand-dollars amp with relays, the risk still exists, so it's always advised to unplug before turning off.
The biggest problem I've found, rather, is the "pop" when you plug your headphones in. It could have been solved with a relay but there is none in the Walnut design as is. My "trick" for this is, when I have them around, to plug some junk headphones I hate in. because the "pop" on plug in only happens to the first set plugged in after power on. So I plug in a bad set of headphones, those get the "pop", and then I switch to different headphones and never is a pop.
I worked this method out after one too many times with my headphones already on, plugged them into the Walnut and got the unpleasant sound. Plus it can't be good for headphones either.
Will the Walnut destroy your headphones? You'd probably have to try pretty hard...
(It is also nice to have these junk headphones around for DIY work, because when building amps you don't always want to plug in a nice set of headphones if you only need to know if it works or not, and don't mind if something is way too loud or otherwise sending harmful signals to the phones...)