Nearly all programs will allow deferral for a Fulbright.
I wouldn’t disclose you are applying until you have been named a finalist/gotten to some competitive stage (e.g. invited for interview). Anybody can apply (assuming you jump through the hoops your specific school expects so you get their support), so the act of going through the process isn’t given any points, and depending on where you’re applying the likelihood of getting it varies so much that schools can’t take into account how likely it is you’ll need to defer.
It was years ago, but I remember letting a school know I had actually received a competitive fellowship abroad and would need to defer and they said “why don’t we see if you get in here first.” This is to say update when you’ve made it to a competitive stage because it is a noteworthy accomplishment, but not before and don’t worry about letting them know deferral plans until acceptance.
