They backup what's on the server. They can't backup what's only on your PC (it could be turned off and they don't have access). And sent mails aren't saved on the server, so not present there. Same for all folders you created yourself in your email client.
Just go into the webmail-interface offered by your mail provider if you don't believe me.
And let me mention a possible disadvantage of incremental backup of your inbox. After 2 years it will contain any mail ever sent to you, including all spam mails you threw away. Restoring your inbox in case something happens will restore that full 2 years of mail. It's a lot of work to sift through it and again delete everything that you already deleted. And I'm afraid your mail archive will grow and grow until you reach the maximum amount of space that was free; than you necessarily start paying unless they have facilities and you have the time to delete all 'old' mails from their archive. You might have to do that manually (a lot of unnecessary work) and it might even be impossible.
But, of course, since it starts being free, it's worth a try. It might be what you need, and then it's a useful tool. But as you see, I'm somewhat skeptical.
Personally, I just copy the Windows folder Thunderbird stores its mail in to another disk. That's a good enough backup for me.