Will leaving the screen of an iPad turned on 24/7 decrease its lifespan?
This is incredibly common for independant cafes and small restaurants using iPads as POS systems. I have personally had several iPads that are literally always on and they have lasted years.

I have also used cheap android tablets for the same purpose and as kitchen displays. They have their place and sometimes make sense but I’ve had to replace them often enough to say that I doubt that you would see a significant cost savings going that route. 

If the outdoor weather proof box gets extremely hot you might see a difference but all the iPads I’ve used have been in fairly harsh conditions with very few problems.