What FF program are you OWE in?
Domestic AA departs from T2 and there is an A/C there, but if you are an AA EXP (OWE) then you will not get access.
Any other OWE will.
If you are travelling in a transcon (ie to JFK) in J/F then by COS rules you will get access, which has nothing to do with being OWE.
I see you are a QP member and that will get you access.