Maybe I should explain my reasons here.  As I understand it Ukyo is living as
a man because of Genma's dishonorable actions.  Because he stole her dowery,
she became a burden upon her family (I'm talking traditional Japanese views
here.  The Ranma bunch are VERY old-fashioned IMHO.)  In order to remove this
burden, she's living as a man.  This explains why she still wears a guys
school outfit after her "comming out" battle with Ryoga.  As I understand it
there are two way that Ukyo can relieve this burden permenantly.  First she
can go through with the original engagement and marry Ranma.  Second she can
be adopted by another family as a girl and they can provide the dowery.
Since the first option is out in my story, Ranma makes the offer for the
Saotome's.  He's sure that he can "persuade" Genma, and doesn't think that
Nodaka would have any trouble with the idea.  Why does he do this?  So that
Ukyo doesn't have to live as a man any more.  He wants to give Ukyo back the
rest of her life.

Alright, with those reasons, would she accept?

I would like to say yes as I think a story of Ukyou becoming Ranma's sister
would
be interesting. However considering the way you have put it I would have to
say No
This would seem to much like charity to Ukyou, She would think it was being
offered as a sop for her feelings out of a sense of charity and not out of
any real affection.
She wants to marry Ranma this would come as a slap in the face. Offering
her an alternative she does not wish.
I think it could be done but you would have to write a story that would
allow Ukyou and Ranma to enter into this new relationship over a course of
time. Build until it is the logical extension of your plot. 
But for him to simply offer it to her as an allternative to marrying him. I
don't think so.
T.H.