Hi Auburn,
I asked the same question to myself during my TT2 project drybuild.
The answer showed itself when I positioned the oil cooler at the front, attached to a replica TT2 front instrument/oil cooler bracket.
The attachment of the oil cooler could not be positioned upside down with the inlet/outlets facing down. There simply isn't the room between the replica TT2 fairing and the oil cooler itself. Otherwise, this would make changing engine oil easier by also draining the remaining oil in the oil cooler. I will provide a picture to explain things.
Attachment:
Fairing2.jpg [ 138.26 KiB | Viewed 1451 times ]
In the case of Graeme's magnificent machine, he has his oil cooler positioned lower (above the horizontal head) so he could run the lines underneath. Only, he has his oil cooler attached conventionally attached Ducati style.
Attachment:
Oil cooler6.jpg [ 311.19 KiB | Viewed 1451 times ]
So, to answer your question....yes, you could run the oil cooler lines however you want. It simply depends where you position it and to what degree of replica your TT2 is/will be....
Hope this helps?
Cheers,
Steve