Neo Toonami has aired 10-year-old anime before. Though that's more common for very old and loved anime like Cowboy Bebop and Ghost in the Shell. Recently, they have focused on getting anime that is as new as possible. We were all surprised when they actually aired Outlaw Star and that wasnt that long ago, so anything can happen really. If Fairy Tail does air starting at Episode 1, no one will care, because not only are those episodes old and are well-seen at this point, but the anime ...... just isn't particularly GOOD. And with newer shonen dominating the front of the block, it likely won't have much of a chance of being a ratings grabber.
You honestly think DeMarco would refuse to air Slime all because of one character? This is the network that aired Kill La Kill, remember.