It doesn't matter if the booster is useable with a lap belt; the FAA rules still disallow any lap-belt-only CRS.
Toddler/booster convertible seats may only be used on board an aircraft if the 5-pt harness is still attached, and when the 5-pt harness is used to secure the child in the seat. If the child is too tall for the maximum harness height (top slots are below the level of the top of the shoulder), then the harness should not be used, as the downward pressure of the straps on the shoulders would contribute to submarining in an impact, or even in a hard-braking situation. Submarining causes nasty internal injuries.
EDIT:
Oh RATS: I just realized that you were talking about carrying the seat onboard, not using it onboard. There used to be a folding booster seat on the market; the name escapes me right now. It hasn't been mfrd since 2000, I think, and in any case, it didn't fold very small. As a general rule, if you want to take a high-back booster on a trip, it will need to go as checked baggage. Most seat-only boosters are small enough to count as a carryon, but even detached, the seatback is usually too big to fit under that standard. You MIGHT be able to separate the pieces of a seat like a StarRiser or a Graco Turbo and put them in the overhead, but I wouldn't want to count on being able to do that. More than likely, it would still be too large and you'd be forced to gate-check it.