This is a good question, and ultimately, the answer is almost certainly no. Getting to that ultimate answer will take some guesswork and assumption. (And, please, no jokes about making an "ass" out of "you" and "umption")
Assuming that Joyce had lived, I find it highly doubtful that she would have stayed in Sunnydale after Buffy's death. Where would she go? I have no clue, but almost certainly Sunnydale would hold too many bad memories for her to stay there, plus, it would certainly have been the last straw in her association with anything vaguely associated with the hellmouth. She would take Dawn and try to start a new life somewhere that didn't have a large portion of its population classified as either undead or nonhuman.
With Joyce gone, even if Willow had still resurrected Buffy, the Slayer would have either gone to be with her mother and sister wherever they had moved, or would have not informed them that she was back, and stayed in Sunnydale to continue her mission there. Either way, it's doubtful that Willow and Tara would have been living with her. They would have remained on campus as roommates in some dorm. They only moved in at Revello Drive to help take care of Dawn. With Joyce and Dawn gone, the house would probably have been sold.
Buffy, if she did, indeed, decide to stay in Sunnydale, would be literally homeless, with no money and nothing except the clothes on her back. She would probably stay with Xander and Anya temporarily, but they really wouldn't have been able to support her indefinitely. Another choice (hang onto your hats, Bangles) would have been moving in with Spike in his crypt. Of all the group, he had the most spacious living quarters, and the only one who could provide Buffy with her own private "apartment," the chamber below his crypt. Remember, she actually seemed to be most comfortable with him when she first returned, and his underground chamber might have even been her idea of the perfect shelter from the harsh, bright, loud, sharp world she had just returned to. I'm suggesting only a place to live, not any sort of romantic involvement here.
Of course, wherever she chose to stay initially, once Giles returned, he would have provided her with quarters, either with him or separately, and no doubt also an allowance for living expenses. Remember, with Joyce still alive and with Dawn in her custody, there would have been no reason to cover up Buffy's death. She would have been declared legally dead, no I D, no Social Security card, and, therefore, no way to get anything but the most menial employment in order to support herself.
Giles would have been able to get the Watchers' Council or someone else to create Buffy a new identity with credentials once he arrived, and with that, she would have been able to find employment and establish her own home.
Willow went dark because Warren accidentally killed Tara while attempting to murder Buffy. With Willow and Tara living either in a college dorm or in their own apartment, they would almost certainly not been near Warren and Buffy at the time of the shooting, so Tara would not have died, giving Willow no reason to go dark.
