I think given the context of the example in the Camel that the behavior is correct. I do think it is a poor example for someone that is new to Perl.
Prior to the example it is stated that suppose we had a file that had \ at the end of a line to indicate that is continued on the next line. This is common in shell scripts. Your examples are assuming that the lines do not have a space before the \ character, again this is not typical in shell scripts. So perhaps a good example of a file would be:

find ./ --name igloo.txt | \
xargs ls -l $1 | \
grep 'Dec'
[download]

Now that is a pointless shell script, but it illustrates the use of the \ at the end of a line that I think might be what the example in the book is refering to.
A more readable example would be:

Hello Cold Cruel \
World. Are you ready
to take a trip to \
the mall with me
for some very delicious ice cream?
I think this will make for a delightful day, \
don't you?
[download]

it would "do the right thing", which is get the next line of the file and append it to the previous lines before it enters the # now process $_ block if the pattern match is a success.

So the eof is needed to prevent it from reading past it, since in effect the redo conditional is superseding the while statement. That is if I am understanding the redo function correctly.

Revised example:

while (<DATA>) {
     chomp;
     if (s/\\//) {
       $_ .= <DATA>;
       redo unless eof;    # don't read past each file's eof
     }
     # now proces $_
     print $_ . "\n";    
   }

__DATA__
Hello Cold Cruel \
World. Are you ready
to take a trip to \
the mall with me
for some very delicious ice cream?
I think this will make for a delightful day, \
don't you?
[download]