Can SQL Server be configured to not silently truncate VARCHAR values?
No there's no way to change this behavior.  But this truncation only happens with variable and parameter assignments, not table inserts.

EG

declare @str varchar(8) = 'some very long string'


will be silently truncated

but an insert:

create table #t(a varchar(8))
insert into #t(a) values('some very long string')


will fail with 

Msg 8152, Level 16, State 14, Line 7
String or binary data would be truncated.


This is a consequence of TSQL's permissive use of implicit conversions, which is convenient in many cases, but sometimes troublesome.