It can still definitely happen since they're bringing in Xbox Live features, so we'll see. There is always the possible issue of latency and lag with online co-op, and Cuphead is a difficult game that's all about precision during those epic boss battles. While they could potentially add online multiplayer co-op for Cuphead with the future cross-play features, we're not sure how well it would perform. This is a given considering that other cross-play games, such as Minecraft, have achievements that sync back to your Xbox Live account.
From what we can gather, the Xbox Live cross-play functionality will include achievements, at the very least.