Mine definitely affects my exhaust sound.. and forget federal law, local law, even without inspections, are very pro-cat. I can't find an exhaust shop in a 100 mile radius that will touch anything catalytic converter forward. If they're certified and get caught (as simple as someone telling on them if THEY get caught) they can face fines up to $10,000 .. at least, that's according to the shops.
If I want a new cat, I *have to* take it to the dealer.. it's sort of rediculous

and when you get a ticket here there is a checkbox for improper exhaust/missing catalytic converter... though I doubt it is enforced, people let their exhaust go without repair even in brand new vehicles.

Hopefully you don't have to face the same kind of laws.. replacement cat can be expensive if the mechanic wants to or has to do it by the book.