Even if you don't have a hard copy or a digital one on your phone with you it's no big deal. As long as you've gone on the website and paid.
Last week, 3 of us were fishing in my boat. A pair of friendly female Conservation Officers pulled along side us. They asked to see our safety equipment, my Boating Card, and all our fishing licenses. They also asked me to open my livewell. All good, except my one buddy had left his Outdoors Card and phone back at the cottage....which he apologized for, but he insisted he did have a valid license which he purchased on-line. The CO asked for his name, date of birth and address...we assumed she was going to write him a ticket. Nope...she got on her phone called in to her office (this was a Sunday), got the admin to search the data base, and verified my buddy did indeed have an up-to-date licence. They wished us luck and went on their merry way.
Very pleasant government employees who just wanted to make sure we were safe, and went out of their way not to fine us.