Yes, if you have the coins in MEW and an exchange has listed it...

Yes, if you have the coins in MEW and an exchange has listed it you just need to get your exchange wallet address and send the coins to that address. When sending a new bunch of coins over to an exchange always do a test first with that coin (for like 10 bucks) to make sure it goes through to your address before sending the rest over.

As long as the coin is listed and you sent to your exchange address the coins you send will automatically go there (may take a number of minutes to hit and go from "pending" to into your account).