> but, sure, advantages compared to other, say, people whose only prior language is Mandarin

I wouldn't understate the significant advantages.

> And, of course, a big disadvantage compared to immigrants who already speak English, even if it's not American English.

Not necessarily. A large percentage of children of immigrants speak with their family (nuclear and extended) mostly in their native language even if their parents can speak decent English. The English skills don't transfer much unless the parents are very active in their child's English education.