I am going to take a wild guess ... since you have goten no answer.

Set up a awstats install 'mutiple_sites'
and in the configuration file point the log's variable to

my @logfile1="/path/logfile1.log";
my @logfile2="/path/logfile2.log";
my @logfile3="/path/logfile3.log";

my @multiple_logs = (@logfile1, @logfile2, @logfile3);
my $log_path = @multiple_logs;

In other words, create an array of the log files then rename that array to the original variable name.

Might work, never tried to make a $string from an @array of log file lines ...

Good coding experiment anyway :P