You need an Internet connection to initially download content. Once Modern Warfare Remastered has been downloaded, you do not need to be connected to the Internet to play/launch the Single Player Campaign or play Multiplayer locally. Will Call of Duty: Modern Warfare Remastered come as a separate disc?
You can play the game offline, but there are several things you need to do first: Install MW3 via disc or download. If you're using a disc, you'll be prompted to download a 70+GB patch. If you purchased a digital download, skip to the next step.