Possible? Yes? Advisable? No. Free flying parrots is really risky and not something you should ever do with your bird unless they are fully & reliably fledged and trained to recall in a variety of situations. Even in the best case scenario, sometimes parrots fly off and are never seen again.
Most āprofessionalā free flyers for this reason only fly their birds in areas with low wind and no tall trees - it makes locating the bird if it fails to recall easier, and ensures that it canāt get too far away from its trainer.
If youāre flying from a balcony Iām assuming this is a multi-unit housing complex, which means lots of places your parrot can decide to land where you canāt retrieve them.