Wither and Despair

Hey Exiles!
I'm building "Caustic Arrow" for the league and for the bosses I was gonna use Wither but then I saw Wither is not a curse, so I said to myself why not both?
So my question is can we use Despair and Wither at the same time?
Technically we should be able to use it like I said Wither is not a curse.
Thanks for the answers.

Thanks for the reply.