The battle will end and the Ho-Oh will disappear. However, it will come back after you defeat the elite 4 again.
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The Poochyena flees when you are one hit away from KO
If Moltres,Zapdos or articuno runs away you need to use action replay to get them back
Normally, you would battle him. He has a Hitmonlee and Hitmonchan, and will give away a Tyrogue upon defeat.
If you run away, you have to beat the elite four. Then, go to the burned tower and suicune will be waiting at the bottom for you. go to serebii.net for a more detailed "how to".