The short answer is yes, but your question implies a fundamental misunderstanding of Bitcoin and blockchains. The coins do not exist "in your wallet" - the wallet just holds your keys that prove you own some of the coins visible to everybody on the public blockchain.
If you want a really great learning aid, search for "Island of Yap Blockchain" and read any of the million articles about it.
If you want a really great learning aid, search for "Island of Yap Blockchain" and read any of the million articles about it.