Stumpokapow
listen to the mad man
Not in every case. I purchased Hungry Cat for my iPhone from the app store awhile back cause the wife loved it. The free version was even in the top 25 downloads for some time. When she got her own iPhone we went to download it and it was nowhere to be found. Gone from the app store as well as my purchase history.
I called Apple about it, and there was nothing they could do. So yeah, if I delete the game it's gone for good.
Another option would be to jailbreak your device and "pirate" the game you've already purchased.