Not naturally, no.
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To get a Tyranitar, you have to catch a Larvitar on 7 island and make it evolve.
No you cannot catch Larvitar in Pokémon Emerald.
I don't think that you can...seeings how its a Jhoto region Pokemon.Do remember, once you beat Pokemon Colosseum/Pokemon XD Gale of Darkness you can trade Pokemon over to Ruby/Sapphire/Emerald if you have a purified Larvitar.But I don't think you can actually catch it IN GAME though.
Try looking in mt silver.
You can catch Larvitar at the Rock PokeSpot on Pokemon XD for the GameCube,You can trade it onto Sapphire after you've beated XD001 (Shadow Lugia)