Not that I've seen. The maxim of taking time off from throwing is more about pitching. From what I've learned, baseball players don't really take time off from throwing but they dial back the workload and don't step on the mound for a couple months. Pitchers still do long toss and flat ground work.
And no problem throwing a football. It's good to build up the muscles supporting the elbow & shoulder.
That being said, no reason to be playing in December at 12. Boys that age need to spend most of November, December, January, and maybe most of February playing other sports or in a S&C program.