I know it’s not an excuse essay, but I am not sure it’s necessary–at all. I’m very sorry to hear about your son’s mom, also. I hope she is doing better.
Again, I think you have to let him decide, but I lean towards no. Here’s why:
“less-than-ideal circumstances, and handled it all well”… shouldn’t that be the norm?
“hard for him to stay motivated”…isn’t that true of most kids?
I’m playing devil’s advocate, but why should he give just the facts about doing what he should have been doing? In general, a kid who has great grades and is still able to play his musical instrument doesn’t have much to explain compared to some kids. The kids who maintain their good grades and still had to work in the grocery store to help support the family during the worst of this pandemic might be the kids who could be expected to fill in the covid supplement. There are other examples, of course.
I do think that it is valid for his guidance counselor to mention in the letter of rec that his mom is afflicted with cancer and that he had to move out of state to live with a relative. Those types of issues are often best mentioned in those circumstances. He can ask the GC if it should be included.