Yes. Assuming you have a command line app (i.e. you own console app) that requires no user interaction you can try the following within your controller method.
Process serverSideProcess = new Process();
serverSideProcess.StartInfo.FileName = @"C:\pathToTheExe";
serverSideProcess.StartInfo.Arguments = "arg1 arg2 arg3";
serverSideProcess.EnableRaisingEvents = true;
serverSideProcess.StartInfo.UseShellExecute = true;
serverSideProcess.Start();
One thing to take note of the Identity of the user account that will execute this process. By default, this should execute server side using the AppPool's credentials. This may be an issue if you need to access network resources. One way to simply overcome this is to let AppPool run under a user account that has been granted access to these resources.