Yes, very much possible:
var consoleOut = new StringWriter();
Console.SetOut(consoleOut);
Console.WriteLine("This is intercepted."); // This is not written to console
File.WriteAllText("ConsoleOutput.txt", consoleOut.ToString());
Later on if you want to stop intercepting the console output, use modification below:
var stdOut = Console.Out;
// Above interceptor code here..
Console.SetOut(stdOut); // Now all output start going back to console window
Or the OpenStandardOutput does the same without the need to save the standard stream first:
// Above interceptor code here..
var standardOutput = new StreamWriter(Console.OpenStandardOutput());
standardOutput.AutoFlush = true;
Console.SetOut(standardOutput); // Now all output starts flowing back to console
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