Once it's successfully uninstalled it is no longer capable of working. However, that does not mean that everything will be back the way it was before you installed it. Some traces will always be left behind (usually a few DLL files, log files, and registry entries), and any malware that came through will remain. In addition, if the port was unblocked so that you could use the P2P software it will remain unblocked until you close it again.
Keep in mind three things:
1.) Scan everything that comes through before opening it...malware is abundant.
2.) Most of the content is illegal, so do the research before downloading.
3.) Your ISP can monitor all traffic and limit your bandwidth if they think the P2P usage is 'over the top.' In addition, their logs can show what was downloaded...keep that in mind concerning #2.