Can you encounter Entei in Pokemon Colosseum?

Question

in pokemon Colosseum can you encounter Entei if you beat him at Mt. battle

Answer 1

• "To Get Entei You need to battle the giant guy at Mt. Battle (you will have to battle nine trainers before him.) Once you get to him you have to battle some of his other pokemon first. He will send Entei out last. Get his HP low and catch him (he is extremely hard to beat)"

http://www.gamesradar.com/gc/pokemon-colosseum/cheats-guides-faqs/g-2005138888000000035339

So to wrap it up, yes. You can.

Answer 2

In order to capture Entei in Colluseum, you will have to battle the Cipher Admin Dakem at Mt. Battle, after area one.
His team consists of Metang, Golem, Swampert, Camerupt, and of course, the Shadow Entei at Level 40.
To easily capture the Shadow Entei, I would reccomend putting it to sleep, paralyzing it or otherwise giving it a status condition, and then throwing Great Balls (they seemed to work better than Ultra Balls throughout the game for me) like crazy.
If you want to, you could also Freeze it, if possible!
So, all in all, you can very easily catch Entei after defeating the boss (bring TONS of revives!).