Hi there, hope you are enjoying BYC!
I disagree about mealworms a being a good addition to the diet for their protein content. While they are relatively high in protein they are also are very high in fat. They are an acceptable treat that is a good source of amino acids and protein, when used in moderation.
Adding them to your chicken feed they would consume it and leave behind frass with no nutritional value to the chickens. Some chicken feeds include diatomaceous earth.. as an anti-caking agent. I have accidentally used chicken feed as bedding before and it had no baring on my mealworms or darkling beetles or the pupa.
Also the chickens would be very likely to pick out the meal worms and toss the chicken feed all over the place, in my experience... and continue doing so to look for more even if they are never added again.
Suffice it to say... I suggest keeping the mealworms separate from your chicken feed and use it as a high value treat they correlate with you.
But you could keep them in chicken feed... I've tried a variety of things from chicken feed, wheat middlings, oats, dog food (not recommended as bedding but okay as a bonus snack), soon they will get the dust from my mini pig feed and probably my chicken feeder if I don't just add a little water and make a mash for them to eat. So many of my feeds leave a lot of feed "dust", I hate to toss it.
I like to use carrots, celery, broccoli stems, and cabbage for moisture as they keep a long time in the fridge. I use cucumber peels or whatever scrap I have also though... fruit like apples and such attract ants or fruit flies to quickly at my location.
True confession...

If you don't maintain the moisture level... they will use each other.

Their wings never help them fly away! Pupa are most vulnerable to being snacked on.
If I were to use an auto feeder and put any moisture on top... generally it will cause molding issues down under. Your mileage may vary. However, I collect my feed and put in rodent proof containers nightly. They also like meal worms.
So I don't THINK it can work. But I like the way you're thinking though! Skip the middle man, eliminate some work, save some space...
Good luck on your adventures!