Yes, despite the letter of the law, there were still slaves held in Georgia during this period.
The article "Slaveholding in Antebellum Augusta and Richmond County, Georgia" (p. 166) indicates a contemporary estimate, in Augusta alone, of about 100 slaves in 1740.
EDIT: It would seem that whatever efforts that were made to enforce the law were not effective in practice, in part because slavery was still legal just over the river in South Carolina.
The prohibition against slaveholding in colonial Georgia was extensively disregarded by South Carolina and Augusta Indian traders and farmers. Cashin correctly notes, "There is little doubt that the farming at Augusta [during the late 1730s and early 1740s] was done by Negro slaves hired from [South] Carolina masters or belonging to traders who had crossed" the Savannah River into Augusta.
In 1741, Thomas Causton, first bailiff of the colony,
wrote that Augustans "have little regard to the act against Negroes or other Laws and do all their planting by slaves."