The short answer is: It is likely available, but at a terrible quality.
Most copies of The Hangover 3 circulating on Tamilyogi are not official studio dubs. Warner Bros. did release an official Tamil dub for some territories, but pirated versions often feature:
If you manage to find the file, you will likely be disappointed. The "Wolfpack" banter loses its edge when the audio sounds like it was recorded in a moving bus.
Amazon Prime holds the streaming rights for The Hangover trilogy in India. While the default audio is English, Prime often includes dubbed audio tracks based on your region. Check the "Audio" selection icon (the speech bubble) while playing the movie. If Tamil is available, you will get a legal, studio-quality dub.
When you watch via Tamilyogi, the creators—the actors, directors, sound engineers, and even the legal Tamil dubbing artists—get paid nothing. If you enjoy Tamil-dubbed Hollywood films, supporting legal platforms encourages studios to dub more movies in the future.