Should VAC banned accounts be able to join the site?

I recently had a problem with a completely dishonest user winning one of my giveaways. I've requested a new winner but I was near the one week deadline to send him the game, so I had to do it anyways. I think about 40% of his giveaways were misleading and when I visited his Steam profile, I've noticed he had been VAC banned. Not to mention that the guy was a douchebag. He stalked me the whole week, asking "where's my key?".

The point I'm trying to make through this very broken english is: It shouldn't come as a surprise that a cheater creates misleading giveaways and tries to take advantage of the system and the community. That being said, should people who've been VAC banned be able join the site?

I know I can (and should) blacklist people like this, but wouldn't it be easier if he wasn't even here winning giveaways in the first place?