Question about wallets and ERC20 coins

If i have an erc20 wallet, cant i theoretically send any erc20 coins to this wallet even if the wallet doesnt currently support that coin? And once the wallet does support it, the coins will appear. Am i understanding this correctly?

Its because im in canada and in january binance is closing here. So i gotta move my coins out. I have a wallet that i really like and i know they'll support the coins in the near future. its an erc20 wallet. I rather move it to this wallet ahead of time rather than going to metamask and then to this wallet adding extra gas fees.

any help appreciated, thanks