If I create a password for my wallet.dat and send it to someone without a password, will they be able to check its balance?
Didn't you initially said your wallet.dat already has already a wallet encryption password/passphrase set by you?
"Someone without a password" doesn't really make sense when you speak of wallet encryption passwords. Or I don't understand you, likely possible. (I think I get what you want to achieve.)
Encrypted Bitcoin Core wallets can be opened and synced without the encryption password/passphrase. As soon as some action is done which needs the private keys to be accessible aka decrypted, Bitcoin Core will demand the entry of the encryption password/passphrase. Such common actions are dumping the private keys or transfering coins from your wallet.
The safety of your coins depend on the complexity and resistance to guess or brute-force your encryption password/passphrase.