NFHS Football & Basketball
Dread Our Coming, Suffer Our Presence, Embrace Our Glory (Solonavi War Cry)
I believe that if there is a carrier (dock, war sun, etc.) in the system, it can support them. If there is no carrier in the system, though, then they do count against the fleet limit.
That is correct.
To be more precise, any Advanced Fighter present that doesn't have support counts against the Fleet Supply. So if you had a Carrier with 4 GFs, and 3 Advanced Fighters in the system, one of those Fighters would count against Fleet Supply.