Can a Bitcoin wallet be identified as belonging to an exchange? Ethereum wallets can be associated with Exchanges (e.g. Etherscan.io will tell you if an address is a Poloniex one).

Is this possible for Bitcoin addresses?
Yes, in theory is possible to guess the ownership of an address to an Exchange.

Notice that I said in theory and I also mentioned that it's a guess. That's because per design each address is anonymous. However, since the blockchain is public, you can analyze the type and amount of transactions getting in and out a specific address and make assumptions based on patterns.

An exchange has generally a large amount of transactions. If they use a finite amount of addresses, eventually transactions will reuse existing addresses.

If you provide a tool or a way for people to publicly share/associate specific addresses with Exchanges, then eventually you will build an archive of matches. I believe this is what Etherscan does.