Apparently, the leech won't wait for you to swallow it, but it'll attach in your aerodigestive tract as soon as it's in it. This case study of children who drank leech-infested water explains pretty well (and in a rather graphical way, in my opinion) what happened to them. I'll copy here just an excerpt (emphasis mine):
A seven year old girl was brought from a remote village (Kamardin Karaiz) with four days history of cough with blood stained sputum after drinking water from a pond. She also developed pain in her throat and was unable to swallow except for liquids. [...]
Her coagulation profile was with in normal limits however her hemoglobin level was 9 g/dl. [...]
On direct laryngoscopy a leech was found attached to the right pyriform fossa with its one end in the glottis which was removed immediately. The patient made a smooth postoperative recovery. On recovery the patient had no dyspnea, stridor or dysphagia and was discharged the next day on oral antibiotics.
This article also reports a historical case of a leech attached into the throat of a Pashtun man in India. The leech was removed with no consequences.
In short, leech ingestion will probably result in having a leech sucking your blood from inside your throat. Although removing it will probably grant a full recovery, it doesn't seem a pleasant experience.