Not if your fare includes a checked bag on some routes: US to Europe: Free. Within the US: ~$45–50 per bike, each way.
How much does United charge for a bike between the US and Europe?
Free (counts as a checked bag). Included in your free checked bag allowance. Basic Economy fares don't include a free checked bag.
How much does United charge for a bike within the US?
~$45–50 per bike, each way. Counts as one of your checked bags. No extra bike fee. Economy fares within the US don't include a free checked bag. First bag: $50 at the airport. Prepaying online is about $5 less.