I posted this question to gtk-perl, and was able to get something that appears to do what I want. To summarize, I found the right signals to watch for to keep the scroll bar at the bottom, unless the user moves it. It reacts correctly when items are added to the tree view, and when the window height shrinks.

I include my final version below for reference. Thanks for the help.

Jim

#!/usr/bin/perl

use strict;
use warnings;

use Glib qw(TRUE FALSE);
use Gtk2 -init;

my($numAdded)=0;

my($win,$tree)=createWin();
Glib::Timeout->add(1000,sub {tickCB($tree)});

$win->show_all();
Gtk2->main();


#
# Creates the widgets in the application.  Returns the main
# window and tree view.
#
sub createWin
{
   my($win,$scroll,$tree,$model,$mustScroll);


   $win=new Gtk2::Window();
   $win->set_default_size(250,300);
   $win->signal_connect(destroy => \&Gtk2::main_quit);

   $win->add($scroll=new Gtk2::ScrolledWindow());
   $scroll->add($tree=new Gtk2::TreeView());
   $tree->set_rules_hint(TRUE);

   $tree->insert_column_with_attributes(-1,'Goo',
      new Gtk2::CellRendererText(),text => 0);
   $tree->set_model($model=
      new Gtk2::ListStore('Glib::String'));

   $tree->signal_connect(
      size_allocate => sub {sizeCB(\$mustScroll,@_)});

   $model->signal_connect(
      row_inserted => sub {rowCB(\$mustScroll,$tree,@_)});

   $scroll->get_vadjustment()->signal_connect(
      value_changed => sub {$numAdded=0});

   addWords($model,100);
   showLast($tree,\$mustScroll);

   return ($win,$tree);
}


#
# Called at regular intervals to add more random "words" to
# the bottom of the tree view.  If the previous word was
# visible beforehand, scrolls the tree view so the new
# words are visible.
#
sub tickCB
{
   my($tree)=@_;

   addWords($tree->get_model(),100);
   return TRUE;
}


#
# Adds random "words" to the bottom of the tree view.
#
sub addWords
{
   my($model,$numAdd)=@_;
   my(@cons)=grep !/[aeiou]/,'a' .. 'z';

   for (1 .. $numAdd) {
      $model->set($model->append(),0,
         $cons[rand @cons] . 'oo');
      $numAdded++;
   }
}


#
# Scrolls the tree view so the last row is visible.
#
sub showLast
{
   my($tree,$mustScroll)=@_;
   my($numRows)=$tree->get_model()->iter_n_children(undef);

   $tree->scroll_to_cell(
      new Gtk2::TreePath($numRows-1),undef,TRUE,0.0,1.0);
   $$mustScroll=TRUE;
   $numAdded=0;
}


#
# Called each time the tree view is resized.  This is where
# we correct the scroll bar, moving it to the bottom if
# appropriate.
#
sub sizeCB
{
   my($mustScroll,$tree,$rect)=@_;

   showLast($tree,$mustScroll) if $$mustScroll;
}


#
# Called each time a row is added to the model.
#
sub rowCB
{
   my($mustScroll,$tree,$model,$path,$it)=@_;
   my($numRows)=$model->iter_n_children(undef);
   my($lastVis);


   if ($tree->realized()) {
      $lastVis=($tree->get_visible_range())[1];
      $$mustScroll=$lastVis &&
         $lastVis->get_indices() == $numRows-2-$numAdded;
   } else {
      $$mustScroll=TRUE;
   }
}
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