Japanese gets away with doing that. So does Chinese - They even give the weekdays numbers. People will adapt and start to think of it as nouns, if you introduce it wide enough.
No it isn’t. If they were named Blorple and Frotz it would be harder than 10. Only because you’ve had your lifetime to learn the order of the Gregorian months is it in any way easier.
Day:Month::Number:Word makes for an easier pattern recognition. It’s the same DD/MM ambiguity problem, but using DD/OCT solves it quite well in conversation and otherwise.