Can I use an ICE/IC train with the Deutschland-Ticket if I know I will reach the destination with a considerable delay?

Yes, you have the right to do so according to statutory passenger rights if the local train has an expected delay of at least 20 minutes. To travel by long-distance train, you must first buy a ticket. The travel costs will then be reimbursed subsequently upon request by the railway company with which you travel, e.g. by the passenger rights service centre of Deutsche Bahn.