You would be able to do what you're looking for, but you may have to install an OS on the external drive for Time Machine to recognize that as a destination. Its not hard to do honestly, but again you'll have to install the OS. Simplest way to do that is connect the drive to the computer and either using the recovery partition or downloading the macOS installer from the AppStore onto the system you'll be able to target the external drive to install the OS (you may even have the option of restoring a Time Machine backup directly from the recovery partition.
If your Time Machine backup is of one of the newer versions of macOS you could be able to boot the computer from the Time Machine backup directly and complete some of the steps outlined above. Ultimately Time Machine is just going to ask where it should restore the backup and I see no reason why an external disk formatted as HFS+ wouldn't show up in said listing.
The only caveat I'd look out for is the inherent risk of using an external drive to boot the computer. A MacBookPro will do it (I've done it for years on client systems and my own for testing and troubleshooting) but you have to be careful to not accidentally unplug the boot-drive when the system is on and running. It regularly won't hurt the computer, but it may corrupt that disk.