To a degree, yes. I don't bind tightly. Never have. I have two binders, primarily. One is an Underworks Cotton Concealer tank, the other is a GC2 binder. I mostly wear the GC2. It still really bothers my ribs - and it's absolutely not too small. Throughout my mid-torso, the fabric is loose around me (and I am small chested so it's not like there's a huge taper or anything). It only does a tiny bit of binding (it's not nearly as strong as the GC2b). Long story short, I've had to stop 3x (twice due to rib sprains, 3rd due to rib strains), and the last time in the fall last year, I decided I'd have to just simply stop binding as much as possible. Now that the weather is warming up, though... bleh.
I'm going to be seeing a physiotherapist for a leg injury next week, maybe I can sneak in my rib issues as well. Assuming you are binding correctly, that might actually be your best bet if surgery is a long ways off.