Oh, and....to answer your thread title question....
Vertical space is important to keep the ventilation as far above their roosting heads as possible. That's about it tho, chickens don't stack well :D
Here's some thoughts on heights...
Yes, just barely.
Only free range, no secure run?
I strongly recommend against this.
It takes up floor space inside the coop.
Oh, and.... Welcome to BYC! @Cluckgirl913
Where in this world are you located?
Climate, and time of year, is almost always a factor.
Please add your general...