I tested this script and — surprise! — it works.

#!perl

use strict;
use warnings;

use Win32::OLE;
use Win32::OLE::Const 'Microsoft Access';

my $database = 'D:\Database.accdb';
my $csv_file = 'D:\Data.csv';
my $tbl_name = 'Data';

my $db = Win32::OLE->new('Access.Application')
    or die "Cannot create Microsoft Access object\n";

$db->OpenCurrentDatabase($database);

$db->DoCmd->TransferText(acImportDelim, '', $tbl_name, $csv_file, -1);

$db->Quit();

exit 0;
[download]

It's remarkably fast, too.

The fifth argument to DoCmd->TransferText is the HasFieldNames parameter. -1 is True, which means the first line of the CSV file is a header.

The missing error checking is on-account-of-because I haven't figured it out yet. But I swear this script is slurping data into an Access database — quickly!