I just crossed the 1,000 night threshold (with 16 years as Diamond) during current stay at a property in Europe. Prior to arrival, I was upgraded to a junior suite on an 11 night stay (significantly more space).
Had some interaction with the GM in the EL a couple of nights before and on the evening after crossing that magic number, I had a nice bottle of local wine and some other goodies. It was not expected, but a very nice gesture. I don't know how long it will take to be in the system officially, and I don't know if this particular property recongizes LTD on a regular basis, but I'll be back next month and will see.
All in all a great experience!