Also, the above (like your original) won't work if anything appears after ">>" on the previous line (including spaces). For example,

>> text
>>> text
[download]

gets changed to

>> text
PYTHON_PROMPT text
[download]

Is that how it should be? Fixing this isn't easy, and it might be impossible without $1

Update: Well, the following doesn't use $1. However, I don't know about effeciency (since I don't have another solution with which to compare). It works, though, which is more than I can say for my attempts that did use $1.

foreach (split("==========\n", <<'__EOI__'))
>>> i = q
==========
YES
>>> i = q
==========
>>> i = q
YES
==========
>>> i = q
>>
==========
>>
>>> i = q
==========
>>> i = q
>> No!
==========
>> No!
>>> i = q
==========
YES
>>> i = q
YES
>>> i = q
==========
>>> i = q
>> No!
YES
>>> i = q
__EOI__
[download]

{
   foreach ($_) {
      if (/\G (?= >>> )/xgc) {
         # Substitution supressed by following ">>".
         redo if /\G >>> [^\n]* \n (?= >> (?!>) ) /xcg;

         # Do substitution.
         s/\G >>>/PYTHON_PROMPT/xcg;

         # Go process next line.
         /\G [^\n]* \n /xcg;
         redo;
      }

      # Substitution prevented by preceeding ">>"
      /\G >> (?!>) [^\n]* \n >>> [^\n]* \n /xcg && redo;
           # ^^^^^ optional due to statement order.

      # Go process next line.
      m/\G [^\n]* \n /xcg && redo;
   }

   print;
   print("==========\n");
}
[download]