I've never grazed rye but I have chopped a lot of it for haylage.  The protein of rye in boot can be near 20% (enough to scour cows) and can fall to below ten in a matter of several days.  Paltability falls quickly as it matures, and fiber climbs quickly.  I don't know how many acres you have, but if you are looking at a window of more than say two weeks, I would really encourage you to try to chop it if possible.