If I were to perform an airdrop (Transfer) with my custom token to addresses holding a different token, would the wallets that my token are being sent to need to be watching it before the transfer to receive it or is that not an issue and they'll be there but just not visible until they watch it?
Without expressing an opinion on the use-case, you could theoretically send ERC20 tokens to an arbitrary list of addresses with some important considerations.
- It could be costly to submit all the transactions (gas).
- They would not know they have control of the tokens. Someone would have to tell them to check the contract.
- Tokens sent to addresses that are not controlled by ERC20-capable wallets would be stranded. I imagine that would include exchange addresses if one naively assumed all holders of token X are implicitly compatible. Non-ERC20 wallets would not be able to spend.
Those are non-trivial issues to work out.
Hope it helps.