Yes, you should be fine for the entire flight. I've always had continuous Gogo coverage on the Q routes across the Gulf.
Here are a few examples of tracks taken by AA flights between PHX & MIA:
http://flightaware.com/live/flight/A...525Z/KPHX/KMIA
http://flightaware.com/live/flight/A...045Z/KMIA/KPHX