What is the data type of the column DocPrepDateTime? If it is a varchar - the it really should be defined as a datetime data type. If it is a datetime data type then you don't need to format.
Is it possible for DocPrepContactName to be a blank/empty string?
You could also do something like this:
Case When nullif(DocPrepContactName, '') Is Not Null THEN coalesce(DocPrepDateTime, getdate()) Else DocPrepDateTime End
Or - you can reverse it, which is simpler:
Case When nullif(DocPrepContactName, '') Is Null Then Null Else coalesce(DocPrepDateTime, getdate()) End
If it is possible for a someone to add a prep contact name - and then remove that value (or blank it out), the above then removes the DocPrepDateTime. If that is not the desired result - then change it to:
Case When nullif(DocPrepContactName, '') Is Null Then DocPrepDateTime Else coalesce(DocPrepDateTime, getdate()) End
As to the error you are getting - if the DocPrepDateTime is actually a datetime data type (as I suspect) then the format you are using is invalid (and isn't needed anyways). In the format statement there are 2 issues - the first being the comma which isn't recognized by SQL Server as a valid date format and fails conversion - and the second problem is for month you need MM and not mm (minutes).
And finally - if that column is a string (varchar) it needs to be changed to a datetime data type. If that isn't possible then you really need to change the format to a non-ambiguous format. MM/DD/YYYY HH:MM:SS will be interpreted as DD/MM/YYYY HH:MM:SS on a system with the language set to British English (for example). A valid format for SQL Server that will always be interpreted correctly is YYYYMMDD HH:MM:SS - and can be returned using CONVERT instead of FORMAT (which is much slower than using CONVERT).