Unless they succeed (as with Haiti), slave rebellions prior to the 19th century actually tend to have the opposite of the effect you described; increased repression of blacks, both free and enslaved, and narrowing of opportunities for a slave to become free or attain better living conditions after such. I doubt Spain would want to incite a slave rebellion in Georgia when they themselves also use slavery on a large scale in the nearby Caribbean.
A slave rebellion in Georgia would not have been possible because slavery was still at this time illegal in the colony. At the Georgia colony's founding in 1732 slavery was outlawed. The slavery ban in Georgia was overturned in 1749, after Georgian whites had 17 years to witness South Carolina whites grow relatively wealthier under a system allowing plantation slavery. Part of the original slavery ban was the concept of social experimentation, preserving labor opportunities for the "worthy poor" of Britain. Another part however was for security against Spanish attack. As a border settlement with Florida, it was thought safer to not have a slave population. But, an outcome of the historic War of Jenkins Ear, despite a Spanish invasion, was a resounding defensive victory at the battle of Bloody Marsh, making the colonists feel pretty secure Spanish invasion would no longer be a concern.
Also, in the OP I am not proposing emancipation or any real lightening of slave codes in any colony where slavery was legal.
In the OP, the Spanish invasion of South Carolina, and the slave uprising it sparks, most likely does not lead to anything but a grim fate of a different sort for the slaves of the area.
[Others have explained Spanish willingness to harbor and arm escaped slaves from english colonies in previous posts. I would only add that Spanish Cuba and Puerto Rico were far less slavery dependent than the plantation colonies of the English, French and Dutch Caribbean, and that the Spanish had ample motive for including servile rebellion in their tactics since their invasion of Georgia in OTL, and South Carolina in the ATL, came only after serial aggression by the British against Spanish Caribbean ports and St. Augustine Florida. In the scenario I am envisioning, the Spanish are trying to devastate South Carolina to screw up the British good]
So, I am thinking that the slave revolt leads to widespread killings, property destruction, burnings, and escapes. I think the Spanish cannot really stick around to hold ground forever and that eventually the British will regain control of South Carolina. But suppression will be messy and take some time. Many, many escapees/revolting slaves will be killed as the British regain control. Others will live on the fringes in escapee or maroon communities for awhile. The luckiest will survive in maroon communities that migrate further away, perhaps up and over the Appalachians. I am not sure if Indian beaver wars had turned Kentucky into a "hunting ground" with minimum permanent population, but one interesting possibility would be if a mass of South Carolina escapes ends up migrating to Kentucky and Tennessee and intermixing with Amerindians and forms a proto-Seminole group.
I figured the white Georgia militia could be heavily called upon to help the suppression of the Spanish invasion and uprising.
The net effect of all this is that the Georgia trustee's initial decision to make Georgia a non-slave colony is validated. It is considered important to have a white buffer on the frontier. Also, South Carolinians, taking some time to recover from property destruction and repopulating themselves, will not be inspiring so much envy among Georgians in the 1740s. So, Georgia goes into the 1750s with some vivid reasons to stick with the no slavery model for awhile.
If this circumstance can be kept up through the beginning of the American revolution, slavery may never start in Georgia, even as it gets fully reestablished in South Carolina.