Well, anything is possible with enough time, money, and effort. But...
I'd say that it would be a huge undertaking and incredibly difficult, and that's an understatement.
1. No matter which QX50 trim you get, the factory stereo is so integrated with the center stack, dashboard, and rest of the car.
2. I'm not even sure you'll be able to fit in a double din sized stereo where the factory stereo controls sit. The controls for the climate system may have to be moved down a bit and the plastic trim for the information screen controls may have to be cut a little at the bottom.
3. It looks like you'd pretty much have to cut into the decorative trim in the center stack.
4. Most cars that can easily accept an aftermarket stereo have trim kits available that adapt the odd geometry of the stereo face in the center stack to a standard single/double din opening. I don't believe there's one out there for the EX35/QX50.
I'm not saying it's impossible, but it would require an incredible amount of custom fabrication to look halfway decent, and that's if it'll even fit in there. If you have an excellent car audio installer with lots of fabrication experience, the wiring diagram from the factory service manual, and a good amount of money, then sure, it can be done. Personally, it wouldn't be worth it for me, but if it's important enough for you go for it

. It would be the first aftermarket stereo install I've seen on this EX/QX50 platform, and I'd truly be interested in seeing both the build process and end result.