To Start. Hello Im new to this sight.

My Question
I have a 2003 s-type 3.0
it had lean faults and mis-fires on all cyl's the car ran rough
it all so had p0420 bank 1 cat inop.
I fixed the vac leaks by replacing the upper and lower intake gaskets,
vac hoses and throttle body gasket.
replaced all coils and plugs. I did not replace the bad cat on bank 1.

will a burnt out cat make the vech still run rough?