Impredicativity + large eliminations (with no excluded middle) in Coq
No: strong elimination of large inductive types (SELIT) is itself inconsistent because it breaks the layering of universes by trivially allowing you to smuggle a large value in a Prop box and take it back out unscathed.
In Is Impredicativity Implicitly Implicit? I proposed a restriction on SELIT which is a bit more permissive than Coq's while still enjoying consistency (I still don't have a proof for it, tho I believe I'm almost there ;-)