GNU sed 17 16 bytes

Thanks to @someone in the comments for pointing out I had this solution backwards, that allowed me to shave off the no-matches check

/\bill[aiouy]/q1

Explained:

/                # Start pattern
 \b              # Match word boundaries
   ill           # Match literal "ill" as start of a word
      [aiouy]    # Match any of [aiouy] directly after
             /   # End pattern
              q1 # If found, exit with status 1, to false as per POSIX