Omitted-variable bias in the constant of multiple regression under heteroskedasticity

Good morning,

I would like to have some deeper information about omitted-variable bias. Here is the real model:

Callback = Constant + b1*Race + b2*Quality + b3*Race*Quality

where Race and Quality are dummies variables and Callback is a rate (between 0 and 1)

If I regress this simple linear model:

Callback = Constant + b1*Race

Race and Quality are not correlated so I know that when adding Quality and Race*Quality it will not correct the omitted-variable bias in b1 (or b1 is unbiased).

Nonetheless, what about the constant ?
Can I say that the constant is correlated with any variable added to the model ? Since the constant is the medium rate when Race = Quality = 0, any variable added which has an impact on Callback has an impact on the constant.

If the answer to the previous question in Yes, can I say that the constant is biased, and then any added variable with an impact on Callback will correct the omitted-variable bias in the constant?

Thanks in advance.