No, because higher treasury rates means a stronger economy, and higher confidence...which will narrow the junk bond spreads over treasuries, and investment grade corporates. It will also help increase the spending on advertising, in the broader economy, and boost cash flows in the media space.
But yes, any "spike" in treasury rates would be a concern. But the Fed's not going to let that happen. They will "talk rates down", if the climbing rates get out of hand.
We're going to be having a "Goldilocks" situation here, imho.