I broadcast mine and I put the fertilizer on at the same time, but I have been told that you can wait for them to come up for about two weeks and then lay the fertilizer down as a top dressing.
I do the same, Nitrogen moves fast through the soil, real fast, the other 2 main elements do not, that is why I like to get it in the ground. Actually, I fertilize just before the last discing pass, this gets the fertilizer a bit deeper, then I disc one more time, broadcast and drag. You can always come back when it is 6" up or so, and top dress with a str8 nitrogen to boost top growth, I have done that a few times when I felt the nitrogen had been already depleted.
I grew a patch of Alfalfa in in the 90s when we had our farm, it did spectacular in a low lying area I had. Used a cultivar A7M came out with, iirc it was Ladak, or dryland alfalfa, but anyway, bred for dryer conditions. Lasted pretty much for the 4-5 years we where still there, though it got thinner each year.