In short yes!

Our son is 2 and has travelled a lot with us and with BA.

Sadly they seem to be experts at losing his boxed car seat (3 times) and also his buggy (twice). They have always been checked at the first wing and have been lost on both short and long haul so at least they are consistent in their approach.

Some of the items have taken weeks to get back to us and one of the car seats has still not been returned to us a year on, but BA have been consistently good at replacing the items with no argument. Ultimately you can’t move a young child easily without a car seat or buggy and despite it often taking a couple of months to actually get the payment, they have always paid out when we have needed to replace.

obviously the usual story of don’t buy excessively expensive ones applies.

hope this helps