Main purpose of CAT is to reduce effects of harmful exhaust gases. CAT is usually removed by mechanics / silencer shop because cleaning it is tricky and kabli is expensive like hash4u mentioned above
without cat engine check light (ECL) will appear again and again. If u have two O2 sensors then fuel average will also be effected. and lastly there will be unnecessary vibration in car .. the only thing that will improve is HP but slightly
u can live without CAT but the unobstructed flow of exhaust gases and continuous vibration is likely to effect something in engine overtime .. i'd personnelly not drive with ECL and a hollow CAT