Wait for Shell to finish, then format cells - synchronously execute a command

Try the WshShell object instead of the native Shell function.

Dim wsh As Object
Set wsh = VBA.CreateObject("WScript.Shell")
Dim waitOnReturn As Boolean: waitOnReturn = True
Dim windowStyle As Integer: windowStyle = 1
Dim errorCode As Long

errorCode = wsh.Run("notepad.exe", windowStyle, waitOnReturn)

If errorCode = 0 Then
    MsgBox "Done! No error to report."
Else
    MsgBox "Program exited with error code " & errorCode & "."
End If    

Though note that:

If bWaitOnReturn is set to false (the default), the Run method returns immediately after starting the program, automatically returning 0 (not to be interpreted as an error code).

So to detect whether the program executed successfully, you need waitOnReturn to be set to True as in my example above. Otherwise it will just return zero no matter what.

For early binding (gives access to Autocompletion), set a reference to "Windows Script Host Object Model" (Tools > Reference > set checkmark) and declare like this:

Dim wsh As WshShell 
Set wsh = New WshShell

Now to run your process instead of Notepad... I expect your system will balk at paths containing space characters (...\My Documents\..., ...\Program Files\..., etc.), so you should enclose the path in "quotes":

Dim pth as String
pth = """" & ThisWorkbook.Path & "\ProcessData.exe" & """"
errorCode = wsh.Run(pth , windowStyle, waitOnReturn)

What you have will work once you add

Private Const SYNCHRONIZE = &H100000

which your missing. (Meaning 0 is being passed as the access right to OpenProcess which is not valid)

Making Option Explicit the top line of all your modules would have raised an error in this case