I used to commute from Boston to Seattle for a client, and often had to take the AS redeye home. They didn't have lieflats, so I would book a window seat and take it with me (only time I used it on a regular basis). I would not stuff it in my rollaboard. Instead, I enclosed it (used a backpacking stuffsack, IIRC) and just hooked it (with a small carabiner) to the outside of my rollaboard. Never had an issue going thru security or boarding. When I wanted to sleep, pulled it out of its cover and shoved it between the seatback and the plane walls. Was enough cushioning for me to catch a few hours ZZZs....better than a neck pillow, at least for me.

HTH