No, it becomes realized when it is sold. They held a bunch of gold that appreciated in value. On paper, they became richer. By selling it that became realized.

No, it becomes realized when it is sold. They held a bunch of gold that appreciated in value. On paper, they became richer. By selling it that became realized. After that, they bought gold again (different type elsewhere but it doesn't matter). That did not make them any poorer; they just converted cash to gold.