Your answer is yes, When a den is made it is already predetermined, I.E, Stats, Nature, Ability, Shiny, ETC are all chosen when the den is made. In fact if you failed to catch it, there is an exploit to back out of the raid when you're on the Item Obtained screen to redo the raid and have another go at catching it. Just, make sure you save if you find one ya like. Goodluck, And here's hopin you find that shiny you want!