Yes! But not very good at it. Up in the freezing north. Nevertheless for me as Hungarian it is a bit surreal to find Hungarian place names elsewhere such as this subset of these lands. (It's incredibly rare, the only similar thing I know of is the Teleki volcano in Africa.) And a bit of Tientsin, China. The blue area in this map. This was the Franz Josef Street. There is a - sadly unsourced and unconfirmed - rumor that Yuan Shikai was an Austrian citizen. Nevertheless his taste in architecture was very much "Ringstrasse" style.

Why not elsewhere? You could largely say that the colonies were inside the Empire. In the sense of poorer, agricultural and resource-providing lands without full rights, administered largely by foreigners not in the local language, in the east/south. Also, too late to the game. Fighting the Ottomans while everybody else was busy sailing away. Vienna besieged by the Ottomans in 1683 - the same year when the British crown colony of New York is divided into 12 counties (suggesting that it was already bustling).