Yes, this can work but not exactly in the way you've planned. Let me explain:
- Yes, you can use TM to backup your computer, but you're not actually backing up a bootable copy of the OS.
- Yes, you can update the OS on your internal drive to macOS Sierra.
- Yes, you can restore the backup from TM to another external HD and use it as a second boot drive. But, before you can do this you will need to install El Capitan on that external hard drive and then boot your Mac from it and migrate your data etc from the TM backup to that drive.
- No, there are no issues concerning software licenses in doing this.
Now, whether this is the best way for you to go about things is up to you. Another option, if you're internal drive has the capacity, is to have two partitions and have El Capitan on one and Sierra on the other.
Yet another option is to use something such as Carbon Copy Cloner or SuperDuper to make a bootable copy of your current system onto an external drive. Once you've tested it and are satisfied all is good, you can then upgrade the internal drive to macOS Sierra. This way you still get the two bootable drives.
If it was me I'd make sure I had a new external drive (in addition to the TM backup drive) and then install a fresh copy of El Capitan on that first. Once that's done, I'd boot up from that and migrate everything across from your TM backup. Then I'd do the upgrade to Sierra on your internal drive.
Once you've got everything working ok on both drives, you'll then want to think about how you manage some of your data. For example, you won't want to maintain two Photo Libraries, two iTunes libraries, etc. So you'll need to think about how you reorganise your files for use regardless of what system you've booted into, which ones will be duplicated or not, and also ensure you have a TM backup of all your data!