If you and your hens lived back when there was no feed available, then yes, you could probably supply them with enough variety to keep them alive.
The big difference is that these days, poultry have been bred to lay way more eggs than poultry back then, so they have much more strict nutritional requirements.
Along with that, I wouldn't say that those poultry thrived back then either. They survived, but our poultry today thrive because of the nutrition we can supply for them.
There was a post a while back about a member who successfully fed her birds on a 100% forage diet. Note that she taught them from chicks to forage food on their own, I'd imagine it would be difficult to do the same for adult poultry. You would also need a lot of acreage, I'd say about an acre per bird.
The short answer is no. Its very very difficult to formulate a diet that would be sufficient for modern day laying hens. You wouldn't be able to do it with simply vegetables and mealworms either. It is so much easier and cost affective to simply purchase a bag of chicken feed. If your looking for a more natural option, you can go for an Organic Non-GMO feed. Even whole grain feed, just note you have to soak or ferment that before feeding.
This thread might interest you. It talks about temporarily formulating a diet for laying hens encase we get a feed shortage, or feed prices start to skyrocket.
I'll grab a link in a second.