I'm sure you can ask, but be prepared for high likelihood of having to pay the fee. If you use a typical bike box (oversize / overweight) there is little way that any check-in agent could justify not having assessed you the fee if asked -- their job on the line.

I guess the question to ask is, "if I were a check-in agent, why would I waive the fee?"

First class, 1K, etc provides only for extra bags without charge, not oversized...