I'm not sure if coinmarketcap.com has had the correct supply: 18,836,593 BTC (as of block 703,865).
CMC is currently showing me a circulating supply of 18,836,656 BTC, which fits with your calculation of all the block rewards added up, so no, it is not showing the actual circulating supply. It also shows the incorrect max supply of 21 million.

There have also been a lot more than 63.25 BTC that have been provably permanently removed from the supply. Given that I linked to a single block which provably burned over 2,600 BTC, combined with 100 BTC overwritten, 50 BTC from the genesis block, at least 30 BTC failed to be claimed by miners, and all the other provably unspendable and OP_RETURN outputs, then the real number would be at least 3,000 BTC.