Hi raffi,
here is the code to Run Appium server programmaticaly with C#
System.Diagnostics.Process process = new System.Diagnostics.Process();
System.Diagnostics.ProcessStartInfo startInfo = new System.Diagnostics.ProcessStartInfo();
startInfo.WindowStyle = System.Diagnostics.ProcessWindowStyle.Hidden;
startInfo.FileName = “cmd.exe”;
startInfo.Arguments = “/C C:\Appium\node.exe C:\Appium\node_modules\appium\bin\appium.js --address 127.0.0.1 --port 4723 --automation-name Appium --log-no-color”;
process.StartInfo = startInfo;
process.Start();
Hope, it will be helpful for you. 
Regards
@Abdul_Sathar_Beigh