Buffy's emotion fuels her with power so if Illyria killed Dawn then Buffy fueled by rage + grief would stand a much better chance of winning, however it would still be close.
Since in the episode of Angel "Time Bomb" we saw Illyria kill Spike, Angel, Wesley and Lorne single handedly i dont think Buffy would not stand much of a chance even with the Scythe.
The question in who would win Buffy with Scythe and Giles, Willow and Xander invoke the powers of the primeval slayer again like in season 4. Buffy's strength, Giles' mind, Willow's spirit, and Xander's heart. All combined into Buffy against Illyria.
Failing that she has her Xander help her. Xander Quote: If you die, I'll just bring you back to life. It's what I do.
In conclusion Buffy alone couldnt win. Fueled by rage and grief maybe. Buffy + Scythe + Primeval slayer power is probably gonna come out on the side of Buffy.
Sorry i rambled on abit there =).