The hay will outgrow the alfalfa, and steal all the moisture, shade out and smoother the new alfalfa.The slow growing young alfalfa won’t have a chance.
It can work if you catch a wet period of several weeks and you really rough up the grass, kill half of it, then get lucky that it catches and the moisture continues. You would have to reduce your hay sod to an oats cover crop in density and growth, which means you won’t have much first cutting hay to baby the alfalfa along.
Not worth the gamble, but someone will say they did it and it worked once. So it is possible, but not a good plan to depend upon.....
I did that to my pasture once, ran a thin field cultivator through it and flung grazing alfalfa seed and fert on it and dragged it. By beating up the grass some of the alfalfa caught and grew, but the results were not impressive after 6 months,, would have been better to solid seed alfalfa on worked ground in strips as grass grows back in on its own as the alfalfa year by year thins.