Okay, first of all, let's agree on our vocabulary.
When you use the acting technique known as "improv", you are "improvising", not necessarily "improving"!!!
Hell no, I wouldn't even consider shooting a movie with all improv. Horrible idea. Will result in absolute disaster.
Every good movie (of any considerable length) stands on a solid foundation of a little thing we call "screenplay". The importance of this cannot be exaggerated.
If your actors/actresses are working from a screenplay, and they change a few words here and there, maybe add something, remove something (with director's approval), that's not necessarily "improv". That's called acting. Most of it happens during rehearsal, but some of it happens, organically, with cameras rolling, and those little improvised moments can be so great.
But to do an entire movie improvised? My God, no!
It is one thing, for an actor/actress to improvise a single line, in the midst of a scene that is strongly written. It is another thing, altogether, to improvise an entire scene! I've done it. It has worked for me. It has also failed, horribly, for me. And on every occasion, it was incredibly difficult, and time-consuming, to edit.
Make an entire movie that way? Jesus Christ, no!