Yes it does.
Some exchanges process withdrawals via smart contracts, and these kinds of transactions are not compatible with all wallets. However you are free to use your Coinomi Ethereum address to receive such withdrawals.
The only difference is that an entry is not generated on your transaction history. But don't worry, the withdrawal is received and does reflect on your final balance.
You can see in the example below, only one transaction is shown for 0.98 ETH, but the total balance is 2.499 ETH. Where does the rest come from? Simple, this account received a deposit of 1.519 ETH via a smart contract. Because of it there is no entry for it on the history of transactions, but the total balance is calculated perfectly.
You can also compare your Coinomi balance with the value shown in https://etherscan.io and see they both match. This transaction type is listed under the "Internal Txns" tab.
When sending from Coinomi, you do not use smart contracts. Transactions from Coinomi are compatible with every service, even ones that don't accept deposits via smart contracts.