No, she was NOT start being trained as a spy by SHIELD at that age; She started at that age in Russia. Hence the whole back story of where she was trained in AOA and Agent Carter.
I do not believe it has been said when she defected.
All that said, I believe the first place she was ever portrayed WITH a Russian accent was in the cartoons. Obviously comics don't have audio, but accents can be implied with the way the dialogue is written, and I do not believe any accent had been written in the books prior to the cartoons.
In Agent Carter the spies were taught with an American accent and watched american TV