I could be wrong but I think that the sides of drawers need to be vertical to make those joints on a table. So you'd probably need to make a different sled (or an attachment) to accommodate that.
Rather than using a sled you might consider just using a square sacrificial push block behind your work, to keep the job square to the fence. Hold your material tight to it and ride the block against the fence. There's a couple of advantages: The bit doesn't need to be extended as far and the tear-out is reduced by the block.
Getting back to your question: Phenolic or cast acrylic or would probably be strong enough as long as the clamp isn't too far from its mounting point.
Rather than using a sled you might consider just using a square sacrificial push block behind your work, to keep the job square to the fence. Hold your material tight to it and ride the block against the fence. There's a couple of advantages: The bit doesn't need to be extended as far and the tear-out is reduced by the block.
Getting back to your question: Phenolic or cast acrylic or would probably be strong enough as long as the clamp isn't too far from its mounting point.