They eventually start to oxidize, but that's a longer/slower process than rotting. It's more important to make sure you get them dry enough than to worry about getting them packaged fast. The biggest downside to overdrying is that they get really brittle and fall apart.
References I've seen indicate that just about all hops maintain at least 50-75% of their oils after 6mo at room temperature so letting them go an extra week during drying isn't going to kill them.