Can FOVE's software installation be automated?

Yes, FOVE's MSI installer (since v0.17) is a standard MSI installer, built with WIX, so it supports relevant standard options:

https://docs.microsoft.com/en-us/windows/win32/msi/standard-installer-command-line-options

Of particular use is the /quiet option. This will disable the GUI and all the of manual input to the installer. We use this internally as well, here's on sample line from an internal C# script:

Utilities.RunProcess("msiexec.exe", $"/i \"{installerPath}\" /quiet");

Note that msiexec.exe is the executable to invoke to install an MSI file.

The SDK itself you don't install on the target machine directly, but rather you bundle the FoveClient.dll (and FoveClient_CLR.dll if using Unity/C#) with your application. You would then add that to your own installer or install process.

Only one runtime should be installed on a PC at any given time, but different applications using different versions of the FoveClient.dll may be installed at the same time, and thus you should avoid conflict by installing the DLLs to a specific location for your app (eg. next to the exe file), instead of in a standard system location.