Keep in mind that the star codes go to the Obi and the Obi does it's thing with it, call forward etc. I found the opposite to be true than what you were told. Experimentally, I attempted to use the providers star codes for speed dial,
VOIP.ms uses a four digit star code. The code hit the Obi and it was rejected.
My guess is that would be that the Obi star codes continue to function and you probably can forget about the the providers. The Obi will probably not pass them.
Of course this is just my observation and I would be thrilled to be enlightened further.
Good Luck!