The only question really revolves around what John of Gaunt would have done to try to have his inheritance in the male line, rather than going to a female heir and thus to whomever she married. If he CAN get the Beaufort line legitimised, then yes he is going to do this, to make a male heir to whatever is entailed. But he no doubt will face opposition from his brothers who are going to be trying to write him out of the equation.
Richard II may oddly have favoured not only legitimising the Beauforts but placing them in the line of succession in this scenario, as doing one but not the other would be illogical if they inherit the duchy. At the time, Richard has no real fear that he will be childless and the question of succession be one to bug him
Actually, without Bolingbroke, it is not unlikely that Richard II's second wife would have borne him children (she would be of age, 12, in 1401)
Best Regards
Grey Wolf