Single application tablet possible?
Theoretically, yes.

I would assume you could accomplish this by the following process:


Root the device. 
Remap every button to the one app you want to run
Configure your device to operate as you want

remove lock screen, etc.

Fill in the gaps


There's where it gets tricky, you could uninstall your launcher as well, but I have not tried mapping buttons to apps (which might require a bit of custom program), and I do not know if you could get to them without a launcher installed, as that is where the system defaults to after rebooting. That being said, removing too much (like the lock screen) could de-stabilize your system, although you may be able to find work arounds for each specific issue (like using No Lock).

This is an interesting idea, and definitely one to play around with. It could yield some interesting applications.