Ironically, not necessarily. If you sent funds to Coinbase's provided address and they wanted to refuse/refund it for some reason, your new owned output would

Ironically, not necessarily. If you sent funds to Coinbase's provided address and they wanted to refuse/refund it for some reason, your new owned output would likely be marked as clean and from Coinbase. This may vary across circumstances of course. And they may decide to refuse to issue a refund.