This is not possible, since steem-engine doesn't allow you to specify a memo message, which would be needed by the exchange to recognize your deposit.
Steem-engine allows users to convert steem-engine tokens and other scot tokens into STEEMP and vice versa. Users can transfer those converted STEEMP to the desired Steem user account in the form of Steem. So, it is clear that users cannot send Steem from steem-engine to bittrex or binance exchange.
However, one can convert STEEMP into STEEM by sending STEEMP to his steemit wallet and and transfer Steem from his wallet to the bittrex or binance exchange.
It actually depends if the tokens from steem - engine you wish to send is already listed on bittrex or binance exchange. If the tokens are listed on binance or bittrex, then you can exchange the tokens directly to your desired crypto. As we all know that most of the tokens on steem-engine were gotten or forked from the steem blockchain which implies that tokens from steem-engine can easily be converted into steem.
Exchanging steem using bittrex or binance is very possible because both exchange platforms have steem listed on their platform. There is actually a direct method of exchanging your steem to other cryptos using bittrex or binance but I sometimes prefer exchanging it to BTC for easy conversion.
Thanks for reading and I hope this helps