When you send a lot of ETH or USDT to a big exchange like Kraken, do they care if its come from a smaller non kyc exchange like Blofin? Do they care if it came from a bridge?
They can be strict or soft with on-chain tracking to find Tainted coins.
Bitcoin Q&A: Blacklists, Taint, and Wallet Fingerprinting.
If you used a small non-KYC exchange, and withdraw it as your deposit to bigger exchanges, I believe that you will have no issue. The exchange from which you withdraw your coin must be not like a P2P exchange or mixers, if you don't want to have problems with your deposits. If you want to avoid risk, don't use these platforms as your temporary storage before you deposit your coin to a big exchange.