NO!
A dead frog on your doorstep means that a cat loves you, is grateful for your kindness (food etc.) and is leaving you a gift.
Frog is pronounced "qing wa". The "q" makes almost a 'ch" noise.
Tiger Balm
frog
CLEANSING,
The Frog
When a tadpole develops into a frog, apart from growing legs and arms, the tail is absorbed into the frog's body.
Kero,
In Chinese, "rana" can be written as "蛙" which means "frog."
Your question should be do the Chinese eat frogs. And the answer is yes they do. My mother, who was from a poor chinese family in the middle of china ate frogs. She loved them.
The correct idiom is "a frog in my throat," meaning that your voice is hoarse and croaking.