Can diverticulitis and diverticulitis cause complications with Crohn's disease?

Maybe. It is possible for underlying ibd to complicate post-operative care of patients requiring segmental colectomy for complicated diverticular disease (i.e. Perforation) especially when it comes to reversal in the setting of active ibd.
Not really. You can have both diseases, with each having potential to cause serious problems on their own. The two do not aggravate each other in any direct way.