Question: I've seen that df -H --total gives me the total space available but only of **mounted** devices, and lsblk gives me the sizes of **all** storage devices, yet not how much space is available within them.

Is there a way I could see the sum total, available storage space of all devices, e.g. hard disks, thumb drives, etc., in one number?

Answer: 
The operation of *mounting* a medium makes the operating system *analyze* the file system. 

Before a medium is mounted, it exists as a block device and the only fact the OS might know about it might be the *capacity*. 

Other than that, it is just a stream of bytes not interpreted in any way. That "stream of bytes" very probably contains the information of used and unused blocks. But, dependent on file system types, in very different places and can thus not be known by the OS (other than mounting and analyzing it)

You could write a specific application that would extract that information, but I would consider that *temporarily mounting* the file system. Standard Unix/Linux doesn't come with such an application.
From the df man page, I'd say "No", but the wording indicates that it may be possible on some sytems/distributions with some version(s) of df.

The other problem is how things can be accessed. For example, the system I'm using right now shows 3 160gb disks in it... but df will show one of them at / and the other 2 as a software based RAID-1 setup on /home.