That link describes how to recover specific files from Time Machine, but it doesn't address your question. The answer is yes, it can. The procedure is very simple. Whether your hard drive died or you're simply installing a new one, install OS X to the new drive. During the installation process the OS X installer should prompt you about migrating data from another computer or source. This is Migration Assistant, which can be used while in OS X even if you skip it during the operating system installation. You can direct it to Time Machine, your old hard drive, or a cloned copy of your old hard drive. OS X will then go through the backup, copying all files and settings (including multiple user accounts, excluding the core operating system files that have already been installed and customized to your computer). When finished, your computer will look exactly as it was with your last Time Machine backup.
It's obvious but worth noting that any directories that you have excluded from your Time Machine backups will not be restored if you use Migration Assistant to copy from Time Machine.
I've used this procedure three or four times now when moving computers and installing new drives, and it works flawlessly. It's a huge time saver.