Does a juvenile adjudication for a felony level offense and resulting TYC commitment qualify such that I can charge our young offender with this crime?

An order of adjudication is not a conviction of crime except as provided in section 51.13(d) of the family code. Tex. Fam.Code 51.13(a) only applies to enhancement of punishment. Unless a specific exception is carved out (which I don't see) you can't charge him with felon possessing firearm if all he has is juvenile adjudications.