Yes, you can do that.
The backup and restore procedure described on that page uses the tar
utility, which operates on files; the encryption you would be using operates below that level, meaning anything you restore will the automagically encrypted for you as it is restored.
Where you might need to be careful (and I haven't done this myself, so I'm unsure if it's really a concern) is to avoid overwriting any configuration files relevant to the encryption. As I assume you're using the encrypted LVM installation option in the Ubuntu install routine, this means any configuration files relevant to LVM, as well as potentially any binaries relevant to LVM (if you currently have LVM binaries on your system but they lack the encryption support). (If LVM is not currently installed on your system, then there's almost certainly no problem whatsoever.)
I would add /boot and /dev as additional directories to exclude from your backup; the former will include any kernel modifications necessary for the encryption after you re-install (and which would be blown away should you restore that directory as well), and the latter, well, that's a fairly egregious oversight in the guide itself, and could get you into a lot of trouble since the encrypted LVM will necessarily modify the nodes within /dev, making them wholly incompatible with whatever you try to restore to them.
1
Does http://www.TrueCrypt.org/ provide a suitable in-place encryption solution for you? (Backing up first is still a smart idea regardless of what you decide to do.) Here's a web page that explains how to use TrueCrypt.org with Ubuntu Linux: http://www.linuxandfriends.com/2010/02/03/how-to-truecrypt-setup-on-ubuntu-linux/
– Randolf Richardson – 2011-09-01T16:11:28.627I don't want to use truecrypt. I want to encrypt the entire disk so if my laptop is stolen, the information is safe. Thanks for your response. – Vinh Nguyen – 2011-09-01T16:17:04.123
2TrueCrypt can encrypt the entire disk just fine, why are you ruling it out as an option? It is easy to back up and it can do a whole or a part of a disk and it runs on ubuntu. Why is that not exactly what you asked? – MaQleod – 2011-09-01T16:35:08.050
@MaQleod He's likely ruling it out because it doesn't meet his requirements that it be able to encrypt his entire Linux system -- whole system encryption is only available under Windows, and in-place disk encryption is again only available under Windows. – Kromey – 2011-09-01T18:25:48.220