If you are flying on the contract carrier (which is required in most cases), there is ALWAYS availability - that's part of the government contract, which is even if there is only 1 seat available in Y, it must be available for government travelers. For some government contracts, there are seats available only in Y. For other government contracts, there is both a Y class and a discounted government fare, for which the fare class letter varies by airline. When the discounted fare class is sold out, you are still able to book in Y class. I've been a regular government traveler for 31 years, so I am speaking from experience.