Certified GKH Gardening Expert
They can, yes. Sometimes they will continue to send up suckers. Undiluted Round Up will help kill these roots. You will need to wound the roots/shoots as suggested (normally, people cut the suckers down and use those wounds) and then paint the undiluted Round Up on these wounds. The bigger or more wounds you paint, the better. The roots will suck the Round Up in and it will eventually kill them. You may have to repeat the process a few times to fully kill the roots if the root system is still strong.