I was wondering if it is possible to run sample libraries and sonar, or any other DAW, from an external drive.

Sure is. I run my sample library and wave directory on External Usb 3 drives without issue. Sonar itself is installed on the system drive.

I believe Sonar needs to be on the same drive as the OS (not all of it) the main .exe, exc.
In order to run Sonar exclusively from an external SSD/HDD or Thumb drive, you would need a portable version.
The registry entries that Sonar installs need to be on the main OS along with the Sonars executable.
 
 

I have used an external SSD and spinner, USB 3.0 and USB C, (WD My Passport) as a second drive on my previous laptop for working on project files and it worked really well with a big performance improvement. The SSD would get blazing hot though. I've since bought a new, more powerful laptop with dual drives so I only use the external drives as a backup.

Thank you everyone for your replies.