To say it straight away the chance that tonsillectomy will cure your sleep apnea is 50/50. This surgery, correctly called Uvulopalatopharyngoplasty, removes either the entire uvula, tonsils, pharynx, soft palate, adenoids or parts of it with the aim to remove the obstruction of your air passageways and allow you to breathe freely again.
This surgery works best in the cases where these organs are enlarged.
Additionally, it is important to note that surgery is only for those patients of sleep apnea for whom all other treatments have been exhausted and proven ineffective or insufficient. Thus, it could be a good idea to get a second opinion about having to go to surgery and perhaps going for sleep apnia testing, because sleep apnea can often be resolved by losing excess weight and CPAP (Continous Positive Airway Pressure) devices.
If you do have tonsillectomy it takes several weeks to completely recover from and you can usually have only soft food as your inner parts are very sensitive and healing following the surgery.
Finally, there are plenty reports on various forums and websites where people report tonsillectomy not curing either the entire or part of their sleep apnea, so do not have great expectations. For example in one case the surgery only managed to solve the snoring, but sleep apnea remained and the person still had to use CPAP device.