Generally speaking an airline like UA is likely to have current interline agreements with nearly every other major airline. Unless you're travelling on a low cost carrier that specifically opposes the idea of connecting baggage (e.g. Ryanair/Easyjet in Europe, JetBlue in the US) then I can't see a problem. I certainly wouldn't imagine any issue with members of the big three alliances (including CX, which is a member of Oneworld).