SQL Server 2008 R2 : LDF file size not increasing
I wouldn't expect a copy operation to increase file sizes unless the file size was too small to begin with.  SQL Server will first use unallocated space within data files before growing the file.  Similarly, if the log file is large enough for the operation, that file shouldn't grow either.

Also regarding log space usage, some operations can be minimally logged to reduce logging requirements.  Whether or not your INSERT...SELECT is fully logged depends on the database recovery model and indexes on the target table.