I know Virgin Australia accept them (just in case you ever go to Australia).
The crew will check the tags on the restraint first (NEVER remove them) to ensure it has the correct compliance numbers on it, the parent is to then install it and then the installation will be checked my crew.
Similar restrictions on the childs size as mentioned by a poster above also apply.
If the parent can't install it correct then unfortunately it can not be used.
For disabled or those with medical conditions it is important to note Virgin Australia do carry upper torso harnesses for use when required. Of course these must be booked via the Guest Contact Centre.