Generally, as a rule of thumb, I tend to leave the C drive for the OS only. 

In this instance the C drive will not be suitable as a cache due to the high rate of IOPS and change that will be taking place, and potentially impact the OS running. 

I agree with @dips, it is often recommendation that you should leave some % of the drive empty. This is because, you needed at least 15% free space on a drive so Windows could defragment it.

• Other than this, nothing changes. Kindly attach a new drive and have it formatted and ready for use. If you need help with these steps please let me know.

Here are a couple great links to the Best Practice site and include discussion on the Cache design, sizing, etc.  It is definitely recommended to have its own drive.

WAN Accelerators - Veeam Backup & Replication Best Practice Guide

WAN Accelerator - Veeam Backup & Replication Best Practice Guide

I tend to find the helpcenter documents focus less on what’s “best” and more on “what’s possible”.

Is it possible to place the cache on C? Yes!

Will it be unsupported placing the cache on C? Nope!

So helpcenter don’t need to complicate further by mentioning anything about the C drive.

But does it mean your OS will be responsive still if you fill your disk in which the cache resides when it’s not the C drive? Yes!

Does using a dedicated drive prevent issues such as Windows update downloading patches that fill the disk and make your backups fail? Yes!

So it’s for reasons like that we don’t recommend using the C drive, I always deploy cache to a dedicated disk. But Veeam will still support you if you can’t do this.