Can I just have VS 2012 version of FxCopCmd or Team Tools installed on TFS 2010 and would that provide same results as that of running CodeAnalysis on VS2012? (Code Analysis in VS2012 in turn uses FxCopCmd)
Yes, this is possible. You will need to specify a CodeAnalysisPath property value that points at the correct path, but otherwise the only concerns should be around licensing, not technical issues.