The main purpose of the EGR is to allow some exhaust gas to recirculate back into the intake manifold when the car is under power. The overall effect is to lower the exhaust gas temperature, which reduces the formation of NOx and SOx compounds.
With the EGR disconnected, you should get a ‘Check Engine’ light come on for an EGR trouble code. Also, this will make the catalytic converter work harder due to higher exhaust gas temps and more NOx compounds than it was designed to handle. Converter burn-out is a real possibility. Also, I pity the exhaust valves. They are getting punished as well. Basically, this can wind up costing more than fixing the EGR, if that was really a problem.
BTW, is the CEL on? It should have gone on before you finished the first drive.