My wife and I (both BA emerald) travelled HKG-CEB with our 4 yr old son (BA sapphire) and 6 month old infant (no FF). We had booked premium economy. Whilst at the Pier F lounge, I was paged and offered an upgrade to J. They were clear that only I could be upgraded and my wife couldn't have the upgrade instead of me (as she had our infant attached to her name in the booking). I offered to let my wife have the upgrade and for me to sit in PEY with the boys, but she passed!
What was interesting is that the lounge staff said that the infant and associated adult could not be upgraded, even if The associated adult were emerald or even CX diamond. It's only for a finite amount of time that we will have this issue, so I guess no big deal.
Has anyone been upgraded with an infant?
No, and afaik it is a rule that infants (i.e. adults with attached infants) will not be upgraded whatsoever, regardless of status.
Edit: IIRC, can't upgrade infants with miles either