Yes, you can use the content-disposition header which will force the Save As..
dialog to the user.
So on your image, you can link to say a handler which will serve the PDF, or perhaps do a postback in an ImageButton
and then serve the file.
String FileName = "FileName.pdf";
String FilePath = Server.MapPath("~/yourPath");
System.Web.HttpResponse response = System.Web.HttpContext.Current.Response;
response.ClearContent();
response.Clear();
response.ContentType = "application/pdf";
response.AddHeader("Content-Disposition", "attachment; filename=" + FileName + ";");
response.TransmitFile(FilePath);
response.Flush();
response.End();