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
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(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";
}
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