I don't think I'm drunk enough for that question to make sense. Gimme a minute.
Right, I think I've got this. HQ is an utter nightmare, temporally speaking. The one time I've tried to make a point-to-point TARDIS flight in here, I ended up six years in the past. Even flights out aren't always safe - this one time, we got dumped in an alternate universe where everyone was a Time Lord. Can you imagine, an entire PPC filled with Time Lords? It was horrible. They made me drink tea.
I don't know that any of my idi- colleagues have tried to deliberately time-travel within HQ. It's possible anyone who did has wiped themselves from history; the original Continuity Council proposal included an Opal President and the Onyx Monitor as a separate position, so there's two candidates for you right away. I might be a bit alarmist about this, but I've had my own experience with erased timelines. I wouldn't try to induce one on purpose.
Unless the Notary's listening. In which case, Spinel Promotor, can you pop back to Event One and pick up my coat for me? I think I left it there.
For that matter, you don't need a TARDIS to time-travel in HQ, which might be what you were getting at. It seems like every time there's a party someone from the past drops in. Perhaps alcohol, in addition to being the foundation of economics, also exerts a temporitational field on local space...?
Ah. Now I'm too drunk for this question.