It depends on the cat. it won't work with the stockers. The converters need heat from the combustion process to "fire off" and start working. If you're too far down stream of the exhaust ports, the cat may not get hot enough to do any work. If it doesn't heat up, it won't function and burn off stuff, causing it to get gummed up and eventually blocked.
There are cats out there that should work usually smaller and will thus wear out faster than stock, but the sizes allows them to heat up further down stream.
When you move the O/2 sensors down, it won't screw up our computers. But what it will do is delay the feedback to the EEC-IV on changes it called for. If anything that'll mess with fuel economy a bit as the EEC-IV will be dealing with larger swings thus not as tight of control.