For starters, his critique ignores what actually happens when a company "moves" overseas or merges with a foreign competitor. The company's tax home may change, but the entire workforce isn't packed up and moved overseas. Some key executives may move, some employees may move, but on the whole, employment decisions will be made based on other factors — like where the R&D facilities are located.
But it's not only common sense that cuts against these arguments. Research evidence does as well.
An industry-funded study from Bates White Consulting suggests that, if anything, after inverting firms in the pharmaceutical space, employment actually increases. (While it's possible that foreign employment rises while domestic employment falls, that's an unlikely outcome). That's not to say that inversions lead companies to employ more people — in fact, these firms were already growing their workforce pre-inversion, and simply continued doing so afterward.