Yes, but with a few remarks. So be advised.

Battle for Caen comes with the newer 50-card decks for the Commonwealth. If you don't own any 2.0 German decks, you or your opponent will have to play a bit differently. It's not a major difference, but still significant.

For the Germans, the scenarios require units from the Big Red One core box. In case you don't have them, you can use first edition units that are 99% similar. There is a conversion chart available in the Big Red One Scenario Booklet.

Big Red One has a few units that were not in the first edition core box. I'd have to check if the scenarios from Battle for Caen use those, but I think you're okay if you are willing to swap units for those missing.