I already have Ubuntu as well as other ways to run and compile source code. Is it necessary to use the appliance to complete the assignments correctly?
Even without an edX account, you should be able to create an account at https://c9.io to use the Cloud9 IDE which the CS50 IDE is based on. And you should be able to create CS50-style IDE with a regular Cloud 9 account.
This would allow you to get a good start on CS50 without using the appliance. However, you will not be able to do all of your assignments if you go this route.
@freshsisyphus mentioned the SPL libraries, which are required for the Breakout problem set. That one is easier to do in the appliance. On the other hand, depending on the version of the course that you take, Breakout may be only present in the Hacker Edition Psets.
Also, in Pset7 (C$50 Finance) and Pset8 (Mashup), you'll be using a the
CS50::query library for PHP, which is a very friendly implementation of something called PDO. This library isn't portable without modification, since it actually requires authentication with edX. (It's possible, and permitted by the license, to comment out the auth code, but that's beyond the scope of the assignments.)
So if the CS50 Appliance is giving you a lot of trouble, it's definitely possible to do most, if not all, of your work in Cloud 9 IDE. I highly recommend creating your c9.io account with your edX credentials, since it will make certain things easier for you later. And by the time you come to the point where the Appliance is required, you might feel much more comfortable with the task.
EDIT: By the way, I am using Debian 8 (Jessie) on my laptop, and I still did all of my class homework in the Cloud9 IDE. (Not counting Breakout, which is a "Hacker Edition" bonus problem, not required.) I found that it was just a lot easier to use Cloud 9 than to get my local C development environment to match the environment of
ide50. Also, I could log into it from other computers, which I found convenient!