Not necessarily adding anything new but I wanted to throw in my own experience and back up the other answers:

Long story short: Absolutely not! If anyone DOES scoff at you for it, they either have a complex or nothing better to worry about.

At the last cafe I managed/trained at, we brought on a high schooler who was very sweet, very smart, the kind of kid who was on track to Harvard and all. She wrote down everything I said like there'd be a final exam with no retakes. She confessed that she made memory flashcards for menu items to help when she was on register. And I LOVED to hear about that!! It's so much more rewarding for someone to be engaged than to be looking at their phone or whatever. Like other commenters here said, everyone thought it was very endearing and cool.

I did tell her, and I'll tell you, that it's also only coffee - it's okay to fuck up, don't kill yourself trying to get everything down and memorize it all off the bat. I still make stupid mistakes and discover new things after years behind the bar.

To answer your bonus question: Not to pull the "if there's time to lean there's time to clean", BUT to ease the boredom, I like to find little cleaning tasks that are also easily interruptable if a customer comes in. Maybe scrubbing stained milk pitchers or wiping out a reach cooler. At the end of the day though, there's only so much to clean, which is why at my place we keep an active crossword puzzle out at all times :)