Do you mean that the opening wouldn't be large enough? I'll be it would be - you know how kitties can get themselves into impossibly small places...But whether they'd find it uncomfortable or not is another question.
I installed a cheap door (no timer) into screening but my girls wouldn't use it. They didn't like the door touching their heads, even though it wasn't heavy. I ended up cutting an opening in the mesh inside the door frame, and they were fine with that. I got the same door for my stray when I moved here, and though it freaked him out a little at first, he got used to it pretty quickly. The first few times he ran through it as fast as he could, but then later he'd stand halfway in and halfway out and not be fazed at all.