Nope!

  DB<128>   $CORE::{substr}
 => *CORE::substr

  DB<129>   $CORE::{print}
 => undef
[download]

It's not really as a "function" in CORE namespace, to rule out overriding.

prototype FUNCTION
               Returns the prototype of a function as a string (or "un
+def" if
               the function has no prototype).  FUNCTION is a referenc
+e to, or
               the name of, the function whose prototype you want to r
+etrieve.

               If FUNCTION is a string starting with "CORE::", the res
+t is
               taken as a name for Perl builtin.  If the builtin is no
+t
               overridable (such as "qw//") or if its arguments cannot
+ be
               adequately expressed by a prototype (such as "system"),
               prototype() returns "undef", because the builtin does n
+ot
               really behave like a Perl function.  Otherwise, the str
+ing
               describing the equivalent prototype is returned.
[download]

  DB<131> prototype 'CORE::print'
 => undef

  DB<132> prototype 'CORE::substr'
 => "\$\$;\$\$"
[download]

Nevertheless can it be called.

  DB<133> CORE::print("bla")
bla
[download]

> I know print is a very special function...

Thats the point, print is magic about indirect object syntax:

eg print STDERR "Fatal!"

This behavior can't be mimiced with normal prototypes, so no STASH entry.