I doubt it. I would have thought that you would need to get the frog out to cure the croak.
In the Celtic tradition, each stream and spring had its own spirit, and frogs were considered the messengers of these water spirits. Because of its connection to rain and water, the frog was also associated with the cleansing and healing powers of water. Frogs eggs were thought to cure rheumatism, and to cure a sore eye, a person only had to lick it after first licking a frog's eye.
The phrase 'a frog in one's throat' is a reference to the croakiness...ie frog-like sound...in the throat brought about by a cold. Click here for a suggestion as to where the idea of an actual frog in the throat as a cure may have come from.