You'll probably get a code from any cat worth having (ie that flows well) but it's not a physical fault. If you can live with it, and maybe a dash light, I wouldn't worry.
Ideally you'd code out the lambda sensor that flags up the 'fault' with a decent stage 2 remap. And ideally the downpipe and cat would be of decent quality. Things like cats can't really be done on the cheap.
I'd consider a second hand oem replacement unless you were serious about doing it right first time.