Yes, PDL::Core (the base class of PDL::Char) overloads almost all, if not all, the basic perl operators so that operations between pdl objects will return a relevant pdl object. This includes operations like != and +.

Just look at this clip of source for PDL::Core to see the complete list:

  use overload (
        "+"     => \&PDL::plus,     # in1, in2
        "*"     => \&PDL::mult, # in1, in2
        "-"     => \&PDL::minus,    # in1, in2, swap if true
        "/"     => \&PDL::divide,   # in1, in2, swap if true
        
        "+="    => sub { PDL::plus     ($_[0], $_[1], $_[0], 0); $_[0]
+; }, # in1, in2, out, swap if true
        "*="    => sub { PDL::mult ($_[0], $_[1], $_[0], 0); $_[0]; },
+ # in1, in2, out, swap if true
        "-="    => sub { PDL::minus    ($_[0], $_[1], $_[0], 0); $_[0]
+; }, # in1, in2, out, swap if true
        "/="    => sub { PDL::divide   ($_[0], $_[1], $_[0], 0); $_[0]
+; }, # in1, in2, out, swap if true

        ">"     => \&PDL::gt,       # in1, in2, swap if true
        "<"     => \&PDL::lt,       # in1, in2, swap if true
        "<="    => \&PDL::le,       # in1, in2, swap if true
        ">="    => \&PDL::ge,       # in1, in2, swap if true
        "=="    => \&PDL::eq,       # in1, in2
        "eq"    => \&PDL::eq,       # in1, in2
        "!="    => \&PDL::ne,       # in1, in2
        
        "<<"    => \&PDL::shiftleft,  # in1, in2, swap if true
        ">>"    => \&PDL::shiftright, # in1, in2, swap if true
        "|"     => \&PDL::or2,        # in1, in2
        "&"     => \&PDL::and2,       # in1, in2
        "^"     => \&PDL::xor,        # in1, in2
        
        "<<="   => sub { PDL::shiftleft ($_[0], $_[1], $_[0], 0); $_[0
+]; }, # in1, in2, out, swap if true
        ">>="   => sub { PDL::shiftright($_[0], $_[1], $_[0], 0); $_[0
+]; }, # in1, in2, out, swap if true
        "|="    => sub { PDL::or2      ($_[0], $_[1], $_[0], 0); $_[0]
+; }, # in1, in2, out, swap if true
        "&="    => sub { PDL::and2     ($_[0], $_[1], $_[0], 0); $_[0]
+; }, # in1, in2, out, swap if true
        "^="    => sub { PDL::xor       ($_[0], $_[1], $_[0], 0); $_[0
+]; }, # in1, in2, out, swap if true
            "**="   => sub { PDL::power     ($_[0], $_[1], $_[0], 0); 
+$_[0]; }, # in1, in2, out, swap if true
            "%="    => sub { PDL::modulo    ($_[0], $_[1], $_[0], 0); 
+$_[0]; }, # in1, in2, out, swap if true
        
        "sqrt"  => sub { PDL::sqrt ($_[0]); },
        "abs"   => sub { PDL::abs  ($_[0]); },
        "sin"   => sub { PDL::sin  ($_[0]); },
        "cos"   => sub { PDL::cos  ($_[0]); },

        "!"     => sub { PDL::not  ($_[0]); },
        "~"     => sub { PDL::bitnot ($_[0]); },

        "log"   => sub { PDL::log   ($_[0]); },
        "exp"   => sub { PDL::exp   ($_[0]); },

            "**"    => \&PDL::power,          # in1, in2, swap if true

            "atan2" => \&PDL::atan2,          # in1, in2, swap if true
            "%"     => \&PDL::modulo,         # in1, in2, swap if true

            "<=>"   => \&PDL::spaceship,      # in1, in2, swap if true

        "="     =>  sub {$_[0]},          # Don't deep copy, just copy
+ reference

        ".="    => sub {my @args = reverse &PDL::Core::rswap;
                        eval {
                            PDL::Ops::assgn(@args);
                        };
                        if ($@) {
                            # Remove references to this (and deeper)
                            # code before rebarfing:
                            $@ =~ s/\s*at .* line \d+\s*\.\n*/./;
                            $@ =~ s/PDL:\s+//g;
                            $@ =~ s/\s*Caught at .* pkg .+\n+//;
                            PDL::Core::barf("Problem with assignment: 
+$@");
                        }
                        return $args[1];
                    },
         
        'x'     =>  sub{my $foo = $_[0]->null();
                  PDL::Primitive::matmult(@_[0,1],$foo); $foo;},

        'bool'  => sub { return 0 if $_[0]->isnull;
                 croak("multielement piddle in conditional expression"
+)
                     unless $_[0]->nelem == 1;
                 $_[0]->clump(-1)->at(0); },
        "\"\""  =>  \&PDL::Core::string   );
}
[download]