Yes. They are legendary. There have been many of each legendary beast shown in the anime, there are events coded into Heart Gold and Soul Silver about creating a new Dialga/Palkia/Giratina, and several trainers have captured and used an Articuno. (Lawrence III, Frontier Brain Noland, Team Rocket.) There are others. Manaphy can explicitly breed. The legendary beasts and birds, Lugia, Celebi, Lati@s, Darkrai, Heatran, the Regis, the Lake Guardians, Victini, Zekrom, Reshiram, and Kyurem (all formes) have been shown to be captured by someone other than the player character of the main series games. In-game, they can all obviously be caught. Heatran live inside volcanoes, and the fanon is that they power said volcanoes. A Latios explicitly died in one of the movies. As far as I know, neither Heatran nor any Regi has died. Moreover, the Regis actually have legends written down about them. Barely any other legendary actually has that.