Yes, you would be pushing the same array ref every time, and the contents would change afterwards.

Test code (no DBI involved):

my @rows;
my @row = qw(one two);
push @rows, \@row;
@row = qw(three four);

use Data::Dumper;
print Dumper \@rows;

__END__
$VAR1 = [
          [
            'three',
            'four'
          ]
        ];
[download]

As you can see, the contents of the collating array changes after you put it in there.