Usually not

Well, maybe so but you really should limit in the case of postgres.

This is basically your example code running against 9.4devel, with and without a limiting where-clause:

$ perl ./tux.pl #  
PostgreSQL 9.4devel_HEAD_20140502_2044_0717748 on x86_64-unknown-linux
+-gnu, compiled by gcc (GCC) 4.9.0, 64-bit

              prepare  execute  finish
 no where     0.00007  5.52991  0.02707
 no where     0.00005  5.42172  0.03283
 no where     0.00005  5.42320  0.03247

where 0=1     0.00005  0.00049  0.00000
where 0=1     0.00002  0.00013  0.00000
where 0=1     0.00002  0.00012  0.00000
[download]

(foo has 10M 1-column rows; just a create table foo as select n from generate_series(1, 10000000) as f(n); )

(What the hell -- let me just dump the test here too, even if it's a bit clunky (disks are cheap and patient):

use strict;
use warnings;
use DBI;
use Time::HiRes qw/gettimeofday tv_interval/;
my $dbh = DBI->connect or die "oops - $!\n";
print $dbh->selectrow_arrayref('select version()')->[0], "\n\n";
my $sql1 = "select * from foo";
my $sql2 = "select * from foo where 0 = 1";
print "              prepare  execute  finish\n";
time_this( $dbh, $sql1, ' no where' );
time_this( $dbh, $sql1, ' no where' );
time_this( $dbh, $sql1, ' no where' );
print "\n";
time_this( $dbh, $sql2, 'where 0=1');
time_this( $dbh, $sql2, 'where 0=1' );
time_this( $dbh, $sql2, 'where 0=1' );

sub time_this {
    my ($dbh, $sql, $how) = @_;
    my $t0;
    $t0 = [gettimeofday];
    my $sth = $dbh->prepare( $sql );
    print $how, "   ";
    printf("  %7.5f", tv_interval($t0 , [gettimeofday]));
    $t0 = [gettimeofday];
    $sth->execute;
    printf("  %7.5f", tv_interval($t0 , [gettimeofday]));
    my @fld = @{$sth->{NAME}};
    $t0 = [gettimeofday];
    $sth->finish;
    printf("  %7.5f", tv_interval($t0 , [gettimeofday]));
    print "\n";
}
[download]

You convinced me, but I was not completely wrong. Unify for example is doing what I said. That is most likely also why my mind thought it was for all databases. Also note that accessing a remote database (see Oracle) diminishes the difference:

All perl-5.18.2 (i686-linux-64int-ld)

psql (PostgreSQL) 9.3.4
DBI-1.631, DBD::Pg-3.1.1
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00011  0.02483  0.00009
where 0 = 1   0.00005  0.00058  0.00001
   no where   0.00004  0.01491  0.00005
where 0 = 1   0.00005  0.00028  0.00000
   no where   0.00004  0.01494  0.00005
where 0 = 1   0.00005  0.00030  0.00001

mysql  Ver 15.1 Distrib 5.5.33-MariaDB
DBI-1.631, DBD::mysql-4.027
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00006  0.01328  0.00005
where 0 = 1   0.00005  0.00021  0.00000
   no where   0.00003  0.01166  0.00004
where 0 = 1   0.00003  0.00014  0.00000
   no where   0.00002  0.01050  0.00006
where 0 = 1   0.00004  0.00017  0.00001

Text::CSV_XS-1.07 (i586)
DBI-1.631, DBD::CSV-0.41
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00026  0.11570  0.00125
where 0 = 1   0.00067  0.08302  0.00000
   no where   0.00037  0.12692  0.00126
where 0 = 1   0.00055  0.07317  0.00000
   no where   0.00028  0.12742  0.00196
where 0 = 1   0.00080  0.08038  0.00000

Text::CSV_XS-1.07 (ia64)
DBI-1.631, DBD::CSV-0.41
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00111  1.01796  0.01366
where 0 = 1   0.00268  0.37951  0.00002
   no where   0.00093  0.54718  0.01354
where 0 = 1   0.00231  0.77326  0.00003
   no where   0.00105  0.64844  0.01313
where 0 = 1   0.00226  0.62751  0.00004

Unify DataServer 8.3
DBI-1.631, DBD::Unify-0.85
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00090  0.00041  0.00014
where 0 = 1   0.00156  0.03468  0.00047
   no where   0.00069  0.00012  0.00002
where 0 = 1   0.00078  0.00695  0.00020
   no where   0.00033  0.00006  0.00002
where 0 = 1   0.00066  0.00828  0.00019

Oracle Database 11g Enterprise Edition Release 11.2.0.3.0 - 64bit Prod
+uction (remote server)
DBI-1.631, DBD::Oracle-1.74
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.02017  0.03333  0.00002
where 0 = 1   0.01903  0.01596  0.00001
   no where   0.01679  0.02241  0.00001
where 0 = 1   0.01580  0.01449  0.00001
   no where   0.01456  0.02465  0.00001
where 0 = 1   0.01581  0.01406  0.00001

firebird-2.5.2.26539
DBI-1.631, DBD::Firebird-1.17
              prepare  execute  finish
------------- -------  -------  -------
   no where   0.00384  0.00001  0.00442
where 0 = 1   0.00375  0.00001  0.00449
   no where   0.00377  0.00001  0.00452
where 0 = 1   0.00382  0.00001  0.00436
   no where   0.00378  0.00001  0.00448
where 0 = 1   0.00377  0.00001  0.00449
[download]

Read more... (3 kB)

Enjoy, Have FUN! H.Merijn