Yes. Except when not. Unless. If.
Sorry for the flippant answers, but you've left some steps out. Briefly, they rely on different reactions at slightly different wavelengths, so you should expect a slightly different response. Each individual protein behaves differently in each case. Compared to a standard curve of the same protein, you should get a similar answer, or maybe the same result, within whatever statistical variation you're capable of working with.
But we need a more complete question, to give you a good answer. If you have an unknown solution of protein, and you cook it up each way and just want an accurate answer, then no, this isn't likely to work. But you shouldn't do it that way in any case.