Can Minecraft be played without being connected to the Internet?

Yes. Once you have logged in at least once with internet connection, you become able to play Minecraft in "offline mode" simply by attempting to log in without internet connection. However, this still requires a paid account to be logged into the computer at some point before.

If you don't want to ever connect his laptop to the Internet, you can copy across your minecraft folder. This is the folder where your saves are stored, along with texture packs and the actual minecraft.jar file which contains the game (as opposed to the launcher) Browse to this folder and copy it to your flash drive. Put it in this same location on his computer. Also, give him a copy of minecraft's launcher. (It's in your home folder, Library, Application Support, Minecraft on a mac, your home folder, .minecraft on linux, or Documents and Settings, your name, Application Data, .minecraft on windows.) It has to be on the same operating system as you are (mac to mac, windows to windows, linux to linux) because even though both are using the same java code they have different natives for sound, etc…. Also, if you want him stuck in offline mode - not able to use your username to get on servers and not accidentally kicking you off when he joins if you are each on separate computers - remove the lastlogin file from the minecraft folder on his computer.

To run it with the saves stored on a flash drive, leave the minecraft folder on the flash drive and create a symbolic link (Mac or Linux) or whatever Microsoft calls it (someone say in comments?) from where the minecraft folder should be to this folder.