In general, the amount of salts or other organic molecules do not affect the solubility of sugar (or any other solute). The solubility of any solute in water is a constant (for a given temperature), as long as whatever is already dissolved does not have any compounds or ions in common with the next solute.

For example, if we wanted to dissolve sodium chloride into a solution of potassium chloride, the amount of chloride already dissolved would affect the amount of NaCl we could dissolve. But if we wanted to dissolve NaCl into a solution of potassium iodide, the KI would have zero effect on the NaCl solubility.

So, since tea has zero molecules in common with the sucrose, the yes shouldn’t affect the solubility of sucrose at all. The only exception would be if solution is acidic, the sucrose can break down into glucose and fructose, of which the tea may have a small (negligible) amount.

Plus we’re not actually saturating the sweet tea. Saturated sugar water is a syrup, so you know just by the consistency that sweet tea is nowhere near saturated.