InnoSetup + MySQL ODBC script = Error Message

Question

The problem lies in your [Run] section. You're going to execute that MySQL ODBC installer from the {src} path. Since you copy your mysql-connector-odbc-5.1.12-win32.msi installer file to the {app} folder, you must run it from the same. Fix your [Run] section of the script this way:

[Run]
; on the following line, run the executable from the {app} directory instead
; of {src}; the {src} folder is the folder in which the Setup files are located
; since it is not an *.exe file, you must also specify the shellexec flag
Filename: {app}\mysql-connector-odbc-5.1.12-win32.msi; Check: IsMySQLOdbcInstalled(); Flags: shellexec
Filename: "{app}\DCS.exe"; Description: "{cm:LaunchProgram,DCS}"; Flags: nowait postinstall skipifsilent

Update:

To meet your additional requirement, run the ODBC driver installer before the main installation process, I've made the following script example (there are kept only parts relevant to the ODBC driver setup).

Anyway, I guess it might be less annoying if you run the ODBC driver installer in some silent mode with some default setting, so it won't offer wizard to the user if there is some (but that's much wider topic for this question; there will be parameters to control the ODBC driver installer, and those you can pass to the second parameter of the Exec function maybe telling the show window flag to be SW_HIDE instead of SW_SHOWNORMAL, which will keep it hidden from user). Please note, this code is untested:

[Setup]
AppName=DCS
AppVersion=1.0
DefaultDirName={pf}\DCS

[Files]
; keep just the only one flag, "dontcopy"; it will tell the installer to not copy
; this file entry to the target machine, but will be part of the setup binary and
; available for manual extracting by using the ExtractTemporaryFile(s) function
Source: "C:\VS12\Projects\DCS\bin\Debug\mysql-connector-odbc-5.1.12-win32.msi"; Flags: dontcopy

[Run]
; remove the ODBC driver installer entry from [Run] section since the [Run] section
; is executed after the installation is succesfully finished and your requirement is
; to run it before the installation process
; Filename: {app}\mysql-connector-odbc-5.1.12-win32.msi; Check: IsMySQLOdbcInstalled()

[Code]
function IsMySQLODBC51Installed: Boolean;
begin
  // the result was inverted in the original code; the original function returned
  // True if the ODBC driver was not installed, False otherwise, and according to
  // the function name it should be vice-versa
  Result := RegKeyExists(HKEY_LOCAL_MACHINE, 'Software\ODBC\ODBCINST.INI\MySQL ODBC 5.1 Driver');
end;

procedure CurStepChanged(CurStep: TSetupStep);
var
  ResultCode: Integer;
begin
  // if we are right before the main installation starts and ODBC driver is not yet
  // installed, then...
  if (CurStep = ssInstall) and not IsMySQLODBC51Installed then
  begin
    // now extract the ODBC installaer to the Inno Setup's temporary folder
    ExtractTemporaryFile('mysql-connector-odbc-5.1.12-win32.msi');
    // and execute the ODBC driver installation (it is necessary to use ShellExec
    // since it is not an *.exe file); if the execution fails, then...
    if not ShellExec('', ExpandConstant('{tmp}\mysql-connector-odbc-5.1.12-win32.msi'), '', '', 
      SW_SHOWNORMAL, ewWaitUntilTerminated, ResultCode) then
    begin
      // show the error message with exit code
      MsgBox('MySQL ODBC Driver setup failed!' + #13#10 + 'Exit code: ' + IntToStr(ResultCode) +
        '; ' + SysErrorMessage(ResultCode), mbError, MB_OK);
      // here you can optionally call Abort to abort the upcoming installation process
      // so if you uncomment the following line, the main installation will not run if
      // the ODBC driver installer execution failed
      // Abort;
    end;
  end;
end;