No, the Cybex cosy is not compatible with the Corolle MGP 36-42 cm Cybex doll pushchair.
The official compatibility only concerns the 36 or 42 cm Corolle dolls and the Cybex Priam 3-in-1 pram structure, but not the Cybex cosy for real babies.
If you need a doll accessory, there's a pram-compatible pram holder/transat, but there's no mention of adaptation for a real Cybex cosy.
I'm not entirely sure, as the information available doesn't explicitly mention the Cybex cosy for a real baby.
For more details, we recommend you consult the official instructions or contact Corolle customer service.

Can the doll's hair cosy be adapted to it?