Yes, this Godaddy hosted server will allow you to run Moodle. The fine print says "Some technical skills needed", however.
I started my website with Godady around 10 years ago using one of these hosted servers, and it worked really well. You can immediately begin moving course content to this Godaddy hosted server, make webpages, and give students access to your course content. This can occur even without Moodle, and it will provide you the ability to learn about your server. I preferred using Dreamweaver for both creating content, and managing my website.
I installed Moodle with the Godaddy "One-Click" install method, and it worked! I used this for about a year. But the problem with the one-click install is that it is initially challenging to figure out how to upgrade Moodle, for a novice. So you can give this a try too, but realize that the learning curve will become a little steep at upgrade time. But sometimes for a novice this is better than learning how to install Moodle on your own. I still own a Godaddy hosted server for experimenting, and Moodle 3.0 runs fine on it.
Eventually, my moodle database exceeded the hosted server's size, so I had to upgrade to a Godaddy VPS. Big learning curve again, but doable.
Today, this is what I have, a Godaddy VPS. I have learned how to install moodle on this severs, and of course, once you know how you wonder why it was hard. Kind of like learning to ride a bicycle.
I am a professor with an interest in using teaching technologies to improve courses for my students, so I don't mind the learning curve(s).
As an alternative, you can also consider getting a free account on the MoodleCloud system. Moodle will work great, but there are some size limitations for the free account. I gave a presentation at this year's MoodleMoot2016 US event about ways to use a (Godaddy) hosted server along with the free MoodleCloud moodle. (Expanding your MoodleCloud Storage to Fill the "Entire Sky")
Moodle is better than any other LMS. But some of the other LMS might seem easier.
Ignore the cPanel website for now. cPanel is included with your hosted server (for free). I actually like cPanel.
How many courses and students per year do you anticipate.