No, it has nothing to do with the size of the main window. In the following code, I made the window wide enough, but still those newly added tabs does not show up.
However, when you click on any existing tab, those new tabs pop up. This is about how and when the window get redraw.
use strict;
use Tk;
use Tk::NoteBook;
my $id = 0;
my $top = MainWindow->new(-title => 'client');
$top->geometry("500x100+0+0");
my $nb = $top->NoteBook()->pack();
$top->Button(-text => "Click", -command => \&add_tab)->pack();
add_tab() for 1 .. 3;
MainLoop();
sub add_tab() {
$nb->add(++$id, -label => $id);
}