Yes I am aware of both types, it was the brutality of the drivers gearchanges that made me hope that it was a dog box, you can shift that quick with a synchro box but only by beating the synchro which results in a graunch that I didnt hear and subsequent damage to the gear engagement flanks, - I have forgotten all the terminology
You cannot double de clutch with a dog box (unless i am mistaken) a heel & toe blip of the throttle could soften things a bit but then you would lose all the time gained in the swift gear change.
I have a motorcycle engined Caterham 7 that I engineered and its the same to a degree with gearchanges on that but there is a lot less inertia in the engine and the gearbox, but more inertia and backlash in the twin propshafts and reversing gearbox, the smoothest gearchanges in that are lightning fast full throttle ones with a momentary lift just at the right time, difficult to get right but never unbalances the car or squalking the tyres, slow gearchanges like on a synchro box sound like you have thrown a bucket of bolts into the transmission.
The dog box Cortina i went in made great clanking noises from the driveline as each gear was engaged because the gearbox input shaft had to instantly change to a very different rotational speed and its inertia, and that of the clutch centre plate resists that, everything clatters including the prop and the diff, with a synchro box it is gradually accelerated and the gearchange made when the rotational speeds are synchronized, unless you beat the synchro. The 2000E box will take quite a lot of that abuse, the type 9 very little before the 3rd gear baulk ring fractures (it has a a narrower section and a stress raiser) which usually leaves you jammed in one gear.
Ask me how I know
I ended up stuck in 4th gear at Lydden hill and had a really epic battle with a backmarker, he would leave me for dead out of the corners and I would get him on the entry to the next one, he said it was the best race he had ever had, I didnt have the heart to tell him of my handicap!