I'm interested to understand why the '|' math operation decided to return a 3 for me, when given two non-numbers to operate on. This was the fun part.

    (3,4,5) | (7,8,9)
=== ((3,4),5) | ((7,8),9)
=== (4,5) | ((7,8),9)
=== 5 | ((7,8),9)
=== 5 | (8,9)
=== 5 | 9
=== 13
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It's a common misconception that (..., ..., ...) is a list. It's simply two instances of the binary operator ",". In list context, "," returns a list consisting of both operands (which are evaluated in list context). In scalar context, "," returns its RHS operand (after evaluating both sides in scalar context).

Is there a way to write this that will work for both empty and non-empty canvas?

Close. Since you're dereferencing ("@{}") the result of the "||", you need to return an array reference on both sides of the "||".

my @list2 = @{ $c->bbox('all') || [ 1,2,3 ] };
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Or if you want to avoid creating an array and a reference to it just so it can be derefenced and listed,

my @list2 = $c->bbox('all');
@list2 = (1,2,3) if !@list2;
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In scalar context, "," returns its RHS operand (after evaluating both sides in scalar context).

That's true except when it's not. See Re^2: ||= oddity

my @list2 = @{ $c->bbox('all') || [ 1,2,3 ] }; does not work because [] evaluates as true in boolean context.

Sorry, but that's not true. It works.

use strict;
use warnings;
use Data::Dumper;
use Tk;

my $t=MainWindow->new();
my $c=$t->Scrolled('Canvas')->pack;
$c->createArc(5,5,100,100);
$t->update;

my @a1 = @{ $c->bbox('all') || [ 1,2,3 ] };
print(Dumper(\@a1));          # 51,3,102,55

my @a2 = @{ $c->bbox('FOO') || [ 1,2,3 ] };
print(Dumper(\@a2));          # 1,2,3
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Because it returns undef (not []) on error as I was assuming.

my $rv = $c->bbox('FOO');
print(Dumper($rv));           # undef
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my @t; my @list = (@t = $c->bbox()) ? @t : (1, 2, 3);
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