The question is applying modern standards of women’s rights and self-determination to a culture that existed long before such inventions. The short answer is that she could not refuse.
Abimelech and Pharaoh were kings in the Bronze Age. One did not refuse Bronze Age kings anything, not as long as one were in their power. The fact that Abraham asked Sarah to agree to this exploit indicated that they lived in a culture in which kings enjoyed whatever women they liked—and if they were refused, and the woman was married, the king who wanted a man’s wife would simply kill the husband. (Sadly, this is what happened with David, Bathsheba, and Uriah.) Thus even less could an unmarried sister or daughter be refused. Unless the visitor were equal in power—as Abraham, although wealthy, was not—refusing would be regarded as a ridiculous and foolhardy insult. Think the medieval right of prima nocta, only even less polite.
It might also help (although it is also unpleasant to reflect on this) to know that women were regarded as mere appendages of men; their value was in bearing and raising children. When Moses counted “all the souls of his [Jacob’s] sons and his daughters” (Gen 46:15) with Leah, and came to the figure 33, guess what? There were 33 males listed, despite the fact that Dinah was just mentioned by name. She was not in the count, despite the count being explicitly of “his sons and his daughters.” Womenfolk were adequately covered by counting the men. Other enumerations such as those in Numbers 1 and 26 similarly omitted the womenfolk.
When Korah, Dathan, and Abiram rebelled against the leadership of Moses, their wives and children were killed along with them (Num 17:27-34). The daughters of the wicked Achan, who stole from the loot of Jericho, suffered a similar fate (Josh 7:24); his wife isn’t even mentioned, so obvious her punishment was, as an appendage of him. Women were a bit more than property, but only a bit.
Sarah was asked to lie to spare Abraham’s life; but when the king’s men came to take her away, rest assured, she wasn’t consulted. Or if she was, it was strictly pro forma.
Do not neglect this explanatory passage in Gen 20, in which Abraham explains to Abimelech why he misled him about the relationship between him and Sarah:
[11] And Abraham said, Because I thought, Surely the fear of God is not in this place; and they will slay me for my wife's sake. [12] And yet indeed she is my sister; she is the daughter of my father, but not the daughter of my mother; and she became my wife. [13] And it came to pass, when God caused me to wander from my father's house, that I said unto her, This is thy kindness which thou shalt shew unto me; at every place whither we shall come, say of me, He is my brother.
She could of course not refuse. That was never a question. The best she could do was to lie to save Abraham’s life.
