I've never disconnected the car seat during flight; especially on a narrowbody, it's pretty unlikely you'll be able to find a place for it. But I also never had any desire to; the car seat is more comfortable for her than the regular seat anyway. And she'd want cuddles some of the time whether in the car seat or not.

In case you don't know, the car seat must be in a window seat on a narrowbody or in a window or inner seat in the middle part of a twin-aisle aircraft to avoid blocking emergency egress. So make sure you have a window seat and the adjacent middle, otherwise no car seat.