Outbound is no issue with the bags, BUT give yourself plenty of time. You have to exit the terminal, walk up to Bradley, clear security. And I do not know if DL can now print a CI boarding pass. If not, you have that step also.

On the return, it does matter who you fly. You claim bags after immegration in order to then clear customs. I THINK they have a bag recheck right after that as you exit customs (I never check bags, so am not certain ).