Yes, it is a common practice to use Twitter for reading only.
You can create a new private account with a random username (not anything that can be linked to you), follow the accounts you're interested in, and do not accept any follower requests.
If you're particularly concerned about privacy, do this with a separate email account (not used for anything else) to reduce the chances of your account coming up in someone's "Friends suggestions" when they upload their contacts to Twitter.
People whom you follow will still be notified that your account follows them, but it won't tell them much if they don't recognize the username.