Yes. Absolutely. Paper losses/gains are real
The reason it is "unrealised" until that point, is that you could instead simply hold until/if the price of Bitcoin (priced in fiat) rises past the level you bought it at, and still sell at a profit (in real terms if you account for inflation, or in nominal terms if you don't).
Then that would be a realised profit.
Hence the distinction between unrealised and realised.