You are going to get a lot of advice and you'll be told the best time to plant alfalfa is in the fall, that the table is stacked against you with a spring seeding.
All mostly true. But, I for one, don't think very far ahead. I hate for it to be spring and think I need to wait until fall to plant a crop that isn't going to bring much if any benefit for a year!?
I can't grow alfalfa here. It's all clover. But, in another life, I managed a couple of dairies in Upstate NY. We'd mostly plant alfalfa in the spring, early as we could get on the ground. And, we'd use oats as a nurse crop. A bushel or more.
Since you want oats only as a nurse crop, don't use more than a bushel. More competes with and reduces the seedling alfalfa survival rate.
So do it! I think you're spot on!
Now, alfalfa is tough! Field and climate ecology need to be just right -- in any season. Good luck!