We had a test pipe on the '81 for several years. When we put a new converter on it I honestly couldn't tell much, if any, difference. A true dual system like Bud's would be a different story.
The air pump is just that, an air pump. It supplies oxygen to the exhaust manifolds to finish burning the unburned fuel that exits out of the exhaust port. It also supplies oxygen to the Cat so it will light off faster. The AIR pump isn't supposed to run with a back pressure as is evidenced by the use of check valves in the system to keep the exhaust back pressure away from the pump. So actually you will be doing it a favor by just letting the converter pipe blow. If you plug it off, it would have to force all it's output through the exhaust manifold tubes which it probably could. These things don't really put out much air. But then they don't need to for the job they do.
The computer worked just as well with the AIR pipe on or off as the cat tube is downstream from the o2 sensor and has no effect on it.