Couple things.

The files do not have DRM on them. They can be played anywhere that regular ripped AAC files can be played.

The only thing tied to your AppleID is the devices connected to use iTunes Match. Essentially you are just logging into your account and acknowledging that you want to have access to everything in the cloud.

What you end up creating is a "master collection" in the cloud that all of your devices can see and access music from. If you are merging several computers that each have slightly different music on them, you will see the combined list after you are done.