This is a hit or miss, but status could make a difference between a phone agent telling you "no, there's no availability" and making a call to the inventory desk to see if space can be cleared.

A few times I've tried to get an F award and one of the segments only had Y. After checking my chances at clearing the waitlist, only to discover an empty F cabin, they called to clear my WL right away. They can do this for anybody, but are more likely to do it for status-bearing members.