Nope, if you go to: https://etherscan.io/ and enter your eth address you can see all the tokens sent to your key. To add them click on "Token Transfers", click on the name of the token, then copy the Contract Address and post that into the "Add token" section on Metamask or on your MEW. Hope that helps!
RE: What exactly is an airdrop? And how do you get started on receiving them?