As experienced by Luks6655, you can't do

(define inferior (inferior-with-channels CHANNELS))

on the top-level of a channel module.  I think the issue is that 
inferior-with-channels is eager (not lazy), so it cannot be used in a 
channel on the top-level, as builds (including channel builds) are 
isolated from the network and have limited access to the file system.

If it would be made lazy, then

(define inferior (inferior-with-channels CHANNELS))
(define-public p
   (package
     [...]
     (inputs (list (lookup-inferior-package inferior "hello")))))

should, in theory, work (unverified).

Greetings,
Maxime.