KYC is applicable for both, fiat and crypto users. Anyways, you can always deposit and play without the need of verifying your account When you hit a win and want to withdraw funds, you'll need to do KYC. BetCoCo can take up to 3 days to verify the accounts, although usually takes around 24 hours 
That is typical true for most of the casino as they won't ask for KYC if you deposit and lose as big money as possible, but if you won some money, they would demand for the KYC. I am not targeting BetCoCo but generally its true with most of the casino. I never get how the gambler playing at the casino benefit from this offer, as withdraw is subject to KYC approval.
My suggestion is to do the KYC first and then deposit and play.
(This is not a financial advice as i usually do not play at new casino until they are proof trustworthy)