This works fine for me with the Easysoft SQL Server ODBC Driver:

use strict;
use warnings;
use DBI;
use Data::Dumper;

my $h = DBI->connect();
eval {
    $h->do(q/drop table mje/);
};

$h->do(q/create table mje (a varbinary(max))/);
my $t = $h->column_info(undef, undef, 'mje', 'a');
DBI::dump_results($t);

my $x = 'a' x 1000;
my $s = $h->prepare(q/insert into mje values(?)/);

foreach (1..15) {
    $s->execute($x);
    print "Inserted ", length($x), "\n";
    $x = $x x 2;
}
$Data::Dumper::Indent = 0;
my $r = $h->selectall_arrayref(q/select len(a) from mje/);
print Dumper($r);
[download]

outputs:

'master', 'dbo', 'mje', 'a', '-3', 'varbinary', 0, 0, undef, undef, '1
+', undef, undef, '-3', undef, 0, 1, 'YES', '0', '0', '0', '0', undef,
+ undef, undef, undef, undef, undef, '37'
1 rows
Inserted 1000
Inserted 2000
Inserted 4000
Inserted 8000
Inserted 16000
Inserted 32000
Inserted 64000
Inserted 128000
Inserted 256000
Inserted 512000
Inserted 1024000
Inserted 2048000
Inserted 4096000
Inserted 8192000
Inserted 16384000
$VAR1 = [['1000'],['2000'],['4000'],['16000'],['32000'],['64000'],['12
+8000'],['256000'],['512000'],['1024000'],['2048000'],['4096000'],['81
+92000'],['16384000'],['8000']];
[download]