C# - Application Running Under A Less Privileged Account Start A Process Executing Another Application Under An Administrative Account?

I am logged in as the administrator when I installed an application named pdflatex.exe on my server. This application works as a converter from LaTeX input file to Pdf file. I host an Asp.net MVC 3 application running under an Application Pool Identity with Load User Profile = True. The Asp.net MVC 3 code contains a code that executes pdflatex.exe using System.Diagnostic.Process instance as follows:

Process p = new Process();
p.EnableRaisingEvents = true;
p.Exited += new EventHandler(p_Exited);
p.StartInfo.Arguments = "-interaction=nonstopmode " + inputpath;
p.StartInfo.WorkingDirectory = @"c:mydomain.comworking";
p.StartInfo.UseShellExecute = false;
p.StartInfo.FileName = "pdflatex.exe";
p.Start();
p.WaitForExit();

From the scenario above, the web application runs under a restricted acount but it executes an external application under a default account that I don't know. Can an application running under a less privileged account start a process executing another application under an administrative account?