Does the Ghost Solution Suite product support TLS 1.2?

Yes, the Ghost Solution Suite product versions 3.1 and newer do support TLS 1.2.

There is a caveat to this however.  Your 32-bit ODBC System DSN for the Altiris eXpress Database Data Source needs to use the SQL Server Native Client 

We don't support any other driver while using only TLS 1.2

To open the 32-bit ODBC go to C:\Windows\SysWOW64\odbcad32.exe.