If you're focusing strictly on the real-world applications of econometric models, then the Applied Econ MS is more than sufficient. Simply put, in an applied econ econometric modelling class, you learn when and how to use these models. In a PhD field course, you mostly learn why these models work (i.e. by deriving asymptotics and the like).
If by Wooldridge, you mean Econometric Analysis of Cross Section and Panel Data, then yes, since it's a first-year PhD text in some places. You should check out Bruce Hansen's Econometrics manuscript. For all intents and purposes, it has the breath and rigour of most PhD textbooks. It's available for free on his website.
However, if you're only concerned with the application of econometric models, you should look into getting Mostly Harmless Econometrics. It's a concise text detailing only the stuff you need to know to work with the models.