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,. Evaluates to false as per POSIX
q (or Q to silence output) is a GNU extension to the program to set the exit status if a condition is matched. See the GNU sed script overview for examples, and the command list for the command's description.