That would be amazing, wouldn't it? It would also nullify the biggest percieved weakness for the Windows Phone platform i.e. fewer apps than those available on either the Android or iOS platforms.
I think your question is one worth asking though. The reason I say this is because certain Android apps do work on BlackBerry's BB10 platform. However, to be able to achieve this compatibility, BlackBerry had to include extra components in their platform.
From a strategic point of view, it probably made sense for BlackBerry to include support for Android apps- the company is in a lot of trouble and they needed to do take some steps to rectify the situation.
In the case of Windows Phone, however, things are different. A year ago, Windows Phone wasn't as well known as it is today. If Microsoft was to decide that it will make Windows Phone support Android apps, that might me Microsoft implying that they don't have any hope that developers will make native apps for Windows Phone.
The difference between Microsoft and BlackBerry is that Microsoft doesn't need to take such extreme measures. They have built a great OS and now the app developers are coming on board too.
Sorry to go off on a tangent but rather than just saying that it is not possible, I figure it might be better to shed some more light on the broader picture.