Well, to be honest TW had only a few routes in the Caribbean (eg MBJ, NAS, SJU) and were just about to start charters to a few others so the larger picture of the region may be little affected (eg BGI, POS). However, to those cities where TW did serve the AA dominance may easily become overbearing. MBJ for instance is served by AA, TW, CO, US, NW and of course JM, plus charters. AA's presence there will certainly be fortified by the merger.
What is true, though, is that TW actually had interest in expanding its Caribbean presence and that will obviously be lost by the AA takeover. CO may expand here a bit, DL is not interested (JM serves its interests) and UA again is uninterested. Put another way, AA will be left in a formidable position to drop (not necessarily add) destinations at its desire, knowing that other US-based competition would be unlikely to fill the gap.
Hop to it, fly for life!