Dialog (and the derived DialogBox) does a non configurable global grab in its Show method so no, other than sub-classing and using a substitute Show method, you can't make Dialog non-blocking.

However, it would be trivial to write your own version of a non-blocking "Dialog" pop up window. Something like this should give you a starting point.

#!/usr/bin/perl
use warnings;
use strict;
use Tk;
my $mw = tkinit;
$mw->update;
my $number;

notify( $mw, "Notification Window #" . ++$number, 4000 );
$mw->repeat( 5000,
    sub { notify( $mw, "Notification Window #" . ++$number, 4000 ) } )
+;

MainLoop;

sub notify {
    my ( $mw, $message, $ms ) = @_;
    my $notification = $mw->Toplevel();
    $notification->transient($mw);
    $notification->overrideredirect(1);
    $notification->Popup( -popanchor => 'c' );
    my $frame = $notification->Frame( -border => 5, -relief => 'groove
+' )->pack;
    $frame->Label( -text => $message, )->pack( -padx => 5 );
    $frame->Button(
        -text    => 'OK',
        -command => sub { $notification->destroy; undef $notification 
+},
    )->pack( -pady => 5 );
    $notification->after( $ms, sub { $notification->destroy } );
}
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