The answer Walter, is yes...downwind... but you want to go to windward.
Lowcountry has it right.
Going east, north or south of Cuba is all into
wind and
current, and the Windward
Passage can get exciting.
I did Panama to Grand Cayman going north in November...basically the same trip as
Jamaica to Panama going the other way.
That would be a very hard trip in a boat with an
outboard if the winds were not friendly and there are some very nasty shallow areas en-route that can get very ugly.
I sailed a light F31 tri with a 15hp
outboard for 6,000 miles, but it would have disintegrated going the
route you choose.