A lot of it depends on the fortunes of war, of course.
However, the people wouldn't have welcomed them as liberators. If the nucleus of Castro's high command survives and returns to the safer areas of the countryside, the US has a though fight ahead.
Unlike in Vietnam, the socialist states would have a hard time sending supplies to the resistance if the US manages to set up a permanent blocade. It's questionable how many Latin American states would support the US in this since they've just invaded a neighbour who commited no outward hostilities against them.
Latin American population would surely grow more hostile against the US and it's possible that this would facilitate more Cuba-like revolutions across the region. With the US stuck in Vietnam as well, this would be fulfilling Guevara's strategy of a global struggle against American imperialism.
The US might put another military figure in charge or they might try to actually form some sort of a broad civilian government, but either of these would likely be seen as a puppet of washington.