From a tech standpoint, it would only be possible for Android apps since Android is a middleware. iOS apps wouldn't be possible because they are native and use direct OS calls to do the job, while on Android you can port the middleware and just redo the connections with a new OS (and that can be already a gargantuan task).
Well, Blackberry did that with Android. But they did that on the same kind of devices that Android runs. Android relies that several tablet/phone specific hardware will be there to use, so it wouldn't work as it is. They would need to fork the Android middleware and change a lot of things. For a company with zero experience with full operating systems, it would be just a disaster.
Despite that, I'm highly sceptical of the interest that people have in apps on their TV. Apple TV success isn't related to millions of apps and Google's Android TV efforts have failed (and the new model is now based on a few key apps). What people want in the TV is only a handfull of apps with video related content (Netflix, YouTube, WWE Network, sports, etc).