The entryway is pretty big and we have put a twin airbed there several times. There is also space to stand it up during the day without being in the way.
Last year DS slept on one in the entry way. We stood it up during the day between the wall and the bed. I do not think there would be enough room between the couch and the bed.
We put one at the foot of the sofa bed next to the wall. There just was enough room to step through to get to the patio door (ground floor) but we managed just fine.
If I remember correctly, there is a night stand between the bed and pullout sofa. So, I think there would be both width and length problems putting a mattress between the two. Perhaps the entry way would work as others suggest.