Can I power my 2012 MBP with the power adapter from my circa 2008 MacBook power adapter, which has a square white box thingy and what I believe is called a "T" connector?
Sure.
If both are 15-inch MBPro, then both will take the larger 85W adapter. The only difference is the routing of the magsafe connector. The older is a "T", and the newer is a right-angle connector. Those are interchangeable.
Remember that the 60W and 85W support different screen sizes. If you do have both the 60W and the 85W, that also means that you have an older 13-inch, and a newer 15-inch. You COULD use the smaller adapter on the larger screen, it will still work, but you won't have enough power for some functions, and battery charging will be very slow, and the smaller adapter (providing more power) can get uncomfortably hot. Don't use that combination for more than a few minutes, and when you have no other choice.