Is the genesis block reward forever unspendable?
There is no technical constraint causing the genesis block's reward to be unspendable forever.
It is a bug that has now become the accepted standard. In the future the genesis block reward could be spent but clients must be updated to fix this bug or they will reject blocks containing a valid input referring to this transaction (4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b).
Other clients outside of bitcoind, like btcd, also mimic this bug so they don't risk a fork if Satoshi ever decided to spend these coins. Seeing that Satoshi isn't around much fixing this bug isn't exactly a priority and there is a good chance that this might never be "fixed".