Yes, the check engine light is what turns on when you have Cel codes from your ecu. I suggest that if you are going to Hollow the cat, to do it properly. Banging out the ceramic isn't enough. there will be pieces lying around the surrounding walls. if you place your cat in there in that condition they will fall apart during the heating process and can make there way into the engine. It sounds fetched but it has happened, I have seen it happen myself. If you have a hammer with a wooden handle, carefully hit the ceramic cone walls until the pieces begin to fall. once you can no longer do it this way, use a wire brush to remove the ceramic in the surrounding wall, wash, and repeat until you can see it is completely clean.
Are you talking about the catalytic converter fitted into the exhaust manifold like this?
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What you could do is look around for an EX header from a 96-00 Civic EX model, get a new catalytic, and do the conversion.
http://www.clubcivic.com/board/showthread.php?t=222404
The O2 sensor on our Civic's are very sensitive, so you'd need to be careful with the catalytic and O2 Sensor. Why do you need to remove the catalytic converter anyways? Is your current one clogged? Cracked? You don't have one at all? If your problem is with the secondary (downstream) o2 Sensor there's a trick for a few bucks that I've used and works, here's the tutorial and explanation: http://www.6crew.com/forum/showthread.php?8613-Spark-Plug-Non-Foulers-as-an-o2-CEL-Fix!
I have never used a strait oem myself, just strait 3" but I doubt deleting the cat will make a ton of recognizable difference to make it sound like "crap". Gains, again not much! at most 1 hp, but he did ask for advise and that's what im giving him if he is going to go forward with it. Spewing out stuff into the air... yes if his engine is in poor condition but it is possible to tune a N/A engine for efficiency to eliminate this. I did it to my rex7 when I had it, most 1st gen rex7 guys do this. its hard but can be done.
