Probably, but at least their tax level is reset to the lowest rate.
The Yanks lose a ton of money pretty consistently over the next few years. Some players leaving will hurt or cost a lot to keep, but it doesn't seem as bad as the Sox schedule of studs reaching free agency in the next few years.
3 years (through 2021)
BOS: Pedey, ERod, Vaz, Barnes, Hembree
NYY: Chapman, Torreyes, Bird
4 years (through 2022 or longer)
BOS: Price, Beni, Devers, Brasier, Swihart, Hernandez, Johnson, Velazquez...
NYY: Severino, Stanton, Judge, Sanchez, Torres, Andujar, Voit, German, Holder, Cessa, Green, Frazier, Loaissiga, Montgomery...
Without even looking at the farm differential, and I think the yanks are better there, here's a look at players under team control for 3 or more years: