While I am actively trying to reduce my email, knowing I will be added to author mailing lists wouldn’t stop me entering multi-author contests.
No, because modern privacy laws mean they always have to offer an easily visible Unsubscribe button, and Gmail makes it easy to block any authors silly enough to not offer that option.
(Or, to put it another way, any author who doesn’t follow the Biblical command to obey the law.)
What does stop me signing up to multi-author contests?
I’m reluctant to enter if too many of the books/authors don’t appear to be Christian fiction, especially if signing up means getting a whole lot of free books I don’t want (e.g. because I don’t read the genre, because they’re books from authors I don’t read … perhaps because they’ve spammed me before, or if they’re books I already have).
The other thing that stops me signing up to some giveaways is geography: paperback giveaways are often US-only because of the cost of posting paperbacks internationally. Even ebook giveaways may not work for non-US readers e.g. if the books are going to be gifted from Amazon.com, that cuts out any readers who can’t access Amazon’s US site because they are required to use their local site (e.g. Australia, Canada, or the UK).