Not going to answer the question directly since I don't know the answer to that exactly, but I will provide some chronology to give you some sort of idea of an answer.

The hammer and sickle was adopted as the symbol for communism by Lenin in 1923.

The Arm and Hammer was adopted as the logo for the socialist party of America in 1904.

The Arm and Hammer logo you know from baking soda was adopted by Church and Co. ever since 1867.

It's a really old idea, it represented Vulcan (God of fire and subsequently the God of smithing) in some points in time, and of course, a very iconic example of a hammer representing and entity is by way of Thor's hammer.

What can definitely be said is that the idea of a arm holding a hammer being a symbol is an idea much older than Lenin.

Sources:

"The Hammer and Sickle: The Role of Symbolism and Rituals in the Russian Revolution"

https://www.westminstercollege.edu/myriad/?parent=2514&detail=4475&content=4797

"Evolution on an Emblem The Arm and Hammer" http://www.academia.edu/231841/Evolution_of_an_Emblem_The_Arm_and_Hammer

According to their website, the logo was created in the 1860s after Vulcan, the god of fire. Since there were no working class or socialist connotations, I'm willing to bet Arm and Hammer never had a problem being considered Soviet. Also, the fact that Arm and Hammer was a huge successful capitalist business makes me think the Soviets wouldn't even want to be associated with it.