The root of the question is really: "Can you run the Android OS on a BlackBerry PlayBook?"
Since one is a Linux derivative and the other is a Unix derivative, it seems a natural fit for here.
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QNX is a microkernel system, with (obviously) mostly POSIX userland interfaces. Linux is a monolithic kernel, with mostly POSIX interface.
The Linux kernel inside Android is heavily modified and configured for the hardware it runs on. It has a lot of non-standard interfaces and devices under its control on your random phone/tablet. Just look at the struggle to get Android derivatives running on the machines. I presume something similar, with other changes, and particular devices, is also valid for QNX on whatever you are contemplating.
Running Android userland over QNX is perhaps possible, but a very large undertaking. Look at the massive work done by the k-FreeBSD Debian (sorry if the spelling is wrong) folks to make a much more similar pair of kernel-userland, where moreover much of the userland was build to be portable, work well together.
Running Android on the machine might be more doable, but you'll lack most (as in "almost all") of the documentation required to use any of the special devices that make the machine worthwile. That is also applicable to the last point.
It would appear that it's not possible, at least according to this thread:
Specifically several users report as follows:
you cannot replace the os on the playbook. case closed. it is protected and has not been broken. as for 2.0 that requires a new playbook with a previous os version that has not been updated.
They are completely different operating systems. Android has very tight dependencies on the Linux kernel. It is built on Linux, not on POSIX. QNX isn't a unix system, but it provides POSIX APIs. That's no help to run Android.
If you have a device that's running QNX, and you want to run Android on it, your only chance is to run a virtual machine in which you run Android, complete with its kernel (which is Linux).
Note that you can run some Android applications on the PlayBook. If you want to run Android, get an Android tablet.
You may be able to run Android on the PlayBook — not on top of QNX, but instead of it. This requires fully jailbreaking the device (i.e. being able to replace the bootloader, not just getting administrator rights in BlackBerryOS), which doesn't seem to be currently possible.