Effect of adding whole egg or yolk to filo pastry?
In my personal experience, adding eggs to dough makes it softer, not crunchier. Adding an egg makes it an &quot;enriched dough&quot; that has the ability to hold onto moisture despite being baked.
Many apple strudel dough recipes include an egg or two in the dough, so you should just go for it.
Finally, while strudel dough is very similar to filo, it is not the same thing, which may be causing some confusion for you.  Per one baking blog:

So the difference is simple, it's the fat! In the Puff Pastry the butter is folded in, in the Strudel dough the oil is part of the dough from the beginning and the Phyllo dough is brushed with oil before being baked.

So per your question, strudel dough sometimes includes an egg, whereas filo (phyllo) never does.