Is it okay to call TryAcquireSRWLock from a thread that has already acquired the lock?

A customer found the MSDN documentation ambiguous. Wouldn't be the first time. In the description of Slim Reader/Writer Locks: An SRW lock is the size of a pointer. The advantage is that it is fast to update the lock state. The disadvantage is that very little state information can be stored, so SRW locks cannot be acquired recursively.