Yes, you can catch Suicune in Pokemon HG, but it is different than Raikou and Entei. In the game, you encounter Suicune many times, but after the last encounter, it moves to a stationary location above Cerulean City.
Suicune is seen in the following places and you must follow it if you wish to capture it. First, it will be found in the north of Cianwood City. After you encounter it there, you will shortly find it outside the entrance of Mt. Mortar in Route 42. Once you find it here, it will leave Johto and head to Kanto where you will see it in Vermillion City soon after you arrive. Next you will see it in Route 14 where it will escape for the final time to be found outside Bill's House in Route 25 after Misty has returned to her gym. This is where you battle Suicune.
If you defeat it and don't capture it, it will re-appear at the Burnt Tower when you beat the Elite Four.
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After Mount Mortar, Suicune will travel to Kanto where you will see it Vermillion City shortly after you arrive on the SS Aqua.
The Shiny Suicune was a game stop event held before Pokemon black and whiter where releases. You had to get either suicune riakou or entei at the event of your Pokemon Pearl/diamond/platinum/soul silver/ or heart gold version, and then transfer them to your Pokemon black/white version.
after you have defeated all 16 gyms go to were you found misty and his boy and suicune will be there.
Beat misty then go to cerulean cape
The pokemon Suicune can be found on Route 25 of the Johto Region. If the pokemon faints or runs away during battle, it is possible to have a rematch at the Burned Tower in Ecruteak City.