I'm not so familiar with HHDL's books but the Gelugpa's Prasangika-Madhyamaka is quite strict to the level of the emptiness of emptiness. Even a relatively real existence of self is denied. There is this concept of self and that's it, nothing beyond that. Just a notion, a false notion. Khedrup Je, the 1st Panchen Lama explains the nature of self in their system,
The fact that if it is searched for in these seven ways (Candrakirti's chariot analysis) no self at all is to be found is what it means for the self to be essenceless. This, however, does not repudiate the fact that, if it is not analyzed, the notion of person is a functional one. It being established by a nominal valid cognition, the person does nominally exist. What is more, when the mind that thinks "I" arises, it does so in dependence on, that is, using as a basis, the five aggregates within one's on continuum [if one is in the form realm or below], and the four, [excluding the form aggregate, if one is a formless being]. Without using [such a basis it would not arise] and that is why it [is said] to be merely labeled in dependence on the aggregates.
(Dose of Emptiness, p. 290)
the relative existence of the person (self) is not denied at all. if it were, you couldnt do the 7 step analysis on it. what the 7 step analysis establishes is the absence of the person existing through its own power (from its own side).
another sign is that functionality is not annihilated upon analysis: "the notion of person is a functional one". a dose of emptiness is a bloody hard book...