When you remove the cats, you'll get a P0420 and P0430 low cat efficiency codes that will be triggered by your rear o2 sensors. Rear o2 sensors play no role in engine control, so your car will run exactly the same with those codes.
Enter MIL Eliminators. The sole function of MIL Eliminators is to keep your check engine lamp off for the codes P0420 and P0430, but won't alter performance. Think of MIL Eliminators as cheap insurance, as if you don't run them, your check engine or SES lamp will always be on, and if something else goes wrong with the vehicle, and triggers another code, you won't know about it, because your check engine lamp will always be on. Plus, having the check engine lamp on all the time is rather annoying.
To summarize your question, look to the above post. Your car will run the same. If you have any additional questions regarding OBDII diagnostics, feel free to post 'em and I'll make sure you get an answer.