No direct experience on access outside of CX's flight times. But it may be a moot point for you anyway. I see that for its inaugural departure tomorrow, the AA flight to DFW will leave from a gate in the main terminal. If that's a permanent feature, the CX lounge on the concourse is a no-go. You can get out there on the tram, but no way for a departing pax to get back to the main terminal.
Frankly you're not missing much. While it's not something to complain about, it's also not the nicest lounge in the CX system by any stretch of the imagination. In the worst case, if AA hasn't made provision for status pax at a contract lounge ICN is still a much nicer airport than most in the U.S. for killing time in the main terminal area.