Yes, it would get rid of it. But unless you take preventative measures, you will end up in the same place you were. You were doing something wrong before. I would get an alternative browser to Internet Explorer, and get a few Anti-Spyware programs. I use Microsoft Anti-Spyware, Ad-Aware SE, and Spybot Search & Destroy. I have Kerio Personal Firewall and Avast! Anti-Virus setup on the parents computer, and it seems to be pretty effective.
Good luck.