For dinner rolls, is there any purpose to mixing egg into the dry ingredients be...

I have an old recipe for no-knead dinner rolls that says:

• Mix flour, salt, instant yeast, and lightly beaten egg.
• Add honey and butter dissolved in warm water.
• Refrigerate overnight.

Is there any purpose to mixing the egg into the dry ingredients before adding the water?

(If not, in order to allow the flour to autolize, would it be reasonable to add an egg and salt mixture half an hour later?)

I'm not looking for rules. I'd like to understand the underlying principles.

There's absolutely no reason to mix the egg in with the flour as opposed to the liquid ingredients, you will get the same result either way. I'd think if anything mixing the egg in with the liquid ingredients will get you a better mix. With no-knead bread you don't need a separate autolyse step as the long proofing time in the refrigerator gives plenty of time for all the enzymes and yeasts to do their thing.

If you did want to convert this to a knead recipe then an autolyse step would be fine, I wouldn't withhold the egg though as getting it mixed in would be challenging, instead I'd mix in the egg with the rest of the ingredients and withhold the salt with a small amount of the water.