I'm thinking it would be nice to partition my C drive (SSD) and use the new drive letter for File History.
Is this possible?
Or will windows not allow using the new partition for File History because it exists on a non-removable drive?
Ultimately the answer is "yes," you can do that. As long as Windows perceives what you are utilizing as a different drive (in this case, your new partition), it should work. It doesn't need to be a removable drive... for example, a network location will also work.
Click on Select Drive
Within that interface, you can potentially select a local drive, choose a network drive by selecting Show all network locations, or manually navigate to a network share by selecting Add a network location
When you have a few minutes to spare, this tutorial explains your potential options a bit more in-depth: