Yes. The point is that when you "trade" BTC for something, you're selling it. We differentiate between a sale and a trade colloquially based on whether currency is involved, but currency isn't that special--its just another good. You realize your gain when you sell your thing in exchange for some other thing.

Moreover, if you bought the toaster, and sold it for $20 in BTC, you would have profited $10 and would need to pay taxes on it.