I would disagree. If you are called away when you should be (the calls you where short should be exercised) this is all written into the price of the conversion, as you have now essentially bought back your short calls at parity. You have only a potential to make money (assuming no upward change in interest rates or downward change in dividend) by not getting called away when you should, or getting called away when your short calls shouldn't have been exercised.
A combo consisting of American options has an explicit sensetivity to volatility, since the calls have additional optionality. Even if nothing has changed in terms of divs and funding, you can see it if the option is right on the early-X boundary the day before the ex-dividend date. PS. Take your favorite model for American options and construct a conversion - you will see that it has some Vega.