Legally it's extremely unlikely that you are allowed to do that as @fbara explained in his/her answer, but you can definitely give it a try and worst case I'd expect the app to be kicked off the store. Seeing as other apps have already done this successfully its not impossible to get done, just not as reliable as using your own assets.
Since icons are nothing more than just an image, yea its definitely possible.
Now about whether or not apple will allow you to use the emojis, I didn't find anything saying that you can or cannot use them. However there are countless apps which already do so, so I assume it should be fine.
Removed line 1 as it probably doesnt answer what the question really was asking