Are Google services backed up by iCloud?
Sorta–but no.

There are actually three different things we're talking about here.


iCloud mail
Storage of attachments in iCloud
Backup


Each of these items are very distinct, but all pull from the same storage pool (your 5GB default.)

Let's go over each.

The first is iCloud mail. This is an email service effectively equivalent to any other, provided by Apple. Depending on when you registered for it (if at all), you'll have either an @icloud.com, @me.com, or @mac.com address. If you're not registered (which is what it appears is the case with your account), you simply don't have one. It's by no means necessary.

The second storage in iCloud. There are two versions of this: the first is temporary storage of large attachments in iCloud. This is a fairly new feature: you may notice if sending an attachment over a certain size that it will ask if you'd like to store it in iCloud instead. The second is just saving attachments you receive, which is pretty self explanatory In essence, this is no different from any other app using iCloud for storage.

The third and final is backup–or rather lack thereof. Backups (at least of iOS devices to iCloud) do not store mail data, as it has to exist somewhere else in the cloud–be it on Apple, Google, or whoever's servers. 

In summary, you aren't using any space for mail in iCloud (unless you told it to, and you can always turn it off.)