That real Alessa has more than a few screws loose. It's understandable she's desperate, apparently pregnant out of wedlock, which is scandalous for a noble woman (or any woman in a historical setting), but her "plan" is still witless. How exactly will the real Brielle take all the blame, huh? She's nothing but a servant being blackmailed by using her sick mother against her. She's guilty of hiding the truth, yes, but in the end she's just a tool. The greatest culprit is the count, who tricked both the duke and the king. It sounds like a situation where the count's eldest son will be inheriting the county sooner than anyone expected.
Certainly, theoretically the real Brielle might lose her head, historical times were ruthless, but she was nothing but an unwilling chest piece in this affair anyway. The real culprits will obviously face their own consequences. Not to mention the real Alessa believing the duke will accept her just like that is hilarious. Why on Earth would he accept the wicked daughter of a lousy man who humiliated him? Considering the duke's personality, I imagine he wouldn't punish the fake duchess at all, but the count would receive no mercy. He's even such a taciturn man that the real Alessa's premarital pregnancy (by some unknown man) would become obvious before anything happened, if for some incomprehensible reason the real Alessa's idiotic plan seemed to work and she got the duchess's position. So, the deal would be broken with an even bigger scandal.