No.
Remember that the YouTube app for iOS first appeared on the original iPhone in 2007. This was before there was an app store for the iPhone, and before YouTube could stream in HTML5 (it only streamed in Flash at the time, and Apple made the decision not to support Flash). Hence, an in-house app was the only option Apple had to provide YouTube to their customers. And it was essential that youtube, given its popularity, be available on Apple's groundbreaking new smartphone.
Nowadays, there IS an app store, Google is able and motivated to build (and devote resources to) its own YouTube app, AND YouTube is watchable on mobile Safari anyway via HTML5. So the Apple-built YouTube app is unnecessary and only a potential drain on Apple's resources (were they to spend any effort maintaining it).
On the Apple TV, there is no other Apple-sanctioned method of watching YouTube Videos (other than Airplay which requires purchasing an additional iOS device). They don't have an App Store and therefore there is no Google-built YouTube option, and Apple doesn't bundle a web-browser with Apple TV so you can't watch them that way either. Hence, like in the early days of the iPhone (and UNLIKE the present-day iPhone), the Apple-built YouTube feature is the only official way to watch YouTube videos on the Apple TV. Apple will certainly not remove the most popular free video-watching option from their set-top streamer. If they open up an app store so that Google can provide its own YouTube app, then sure I could see Apple removing their Apple-built YouTube feature. But so far all the particular features/apps on the Apple TV are built/maintained by Apple, with agreement to the content provider. That is, the Netflix, Hulu Plus, NHL, NBA, Wall Street Journal, etc. apps are built by Apple to ingest content from the third party sources. The YouTube app is no different at this point.