While some wasabi is vegan, many are not.
If you look at enough wasabi in different stores, you’ll find some that have egg whites in them, and some even have lactose (from dairy) added to them for some reason.
Truly authentic wasabi is sometimes made by grinding the root against sharkskin even, although if you live in a western country, you probably won’t run into this kind.
So while some wasabi is vegan, some is not.
Unless you can see the ingredients label yourself, I’d pass on it. Your vegan sushi will be good enough without it!