I'm not clear how you determined that it lacks the FAA approval. I reviewed the link you provided but came up empty. Have you inspected an example of the actual seat? Generally, there will be a sticker on the back of the seat that mentions aircraft approval.
On page 10 of the .pdf owners' manual on the site, it says this:
THIS INFANT RESTRAINT CONFORMS to all applicable Federal Motor Vehicle safety standards and is certified for use in motor vehicles and aircraft.
http://www.gracobaby.com/assets/pdfs.../ISPC065BA.pdf
Looks to me like it's approved. I've actually never encountered a US sold infant or child car seat that wasn't approved (not counting, of course, toddler booster seats lacking their own belt system - those are never approved for aircraft).
Section 8.1 of the manual details how to install on aircraft. I think it's approved.