My game engine tries to allocate large texture arrays to be able to batch majority (if not all) of its draw together. This array may become large enough that fails to allocate, at which point I'd (continually) split the texture array in halves.
Is it bad design to push the boundaries until receiving a glGetError:Out of memory and scale back from there?
Is my application a jerk because it's allocating huge chunks of VRAM, which may require swapping into GTT memory? As in, is it less ideal for the graphics driver to be manipulating a few large texture arrays rather than many individual textures when dealing with other OS operations?
It is hard to evaluate how well drivers handle large texture arrays. Behaviour of different drivers may vary a lot.
While using texture array can improve performance by reducing the number of draw calls, that should not be the main goal. Reduction of draw calls is somewhat important on mobile platforms, and even there, several dozens of them is not a problem. I'm not sure about your concerns and what exactly you try to optimise, but I would recommend using profiling tools from GPU vendor before doing any optimisation.
Is it bad design to push the boundaries until receiving a glGetError:Out of memory and scale back from there?
This is what typically done when data is dynamically loaded to the GPU. Once the error is received, old data should be unloaded to load a new one.
Is my application a jerk because it's allocating huge chunks of VRAM, which may require swapping into GTT memory?
There is no way to check if data was swapped to GTT or not (if driver supports GTT at all). The driver handles it on its own, and there is no access to that from OpenGL API. You may need to use profiling tools like Nsight, if you are using a GPU from NVidia.
However, if you are planning to have one giant textures array, it must fit into VRAM as a whole, it can not be partially in VRAM and in GTT. I would not recommend relying on GTT at all.
It must fit into VRAM, because when you bind it, the driver can not know beforehand which layers will be used and which won't since selection happens in the shader.
Despite the fact that textures array and 3dtexture are conceptually different, at hardware level they work very similarly, the difference is that the first one uses filtering in two dimensions and the second one - in three dimensions.
I was playing with large 3d textures for a while. I did experiments with GeForce 1070 (it has 6GB), and it handles textures ~1GB very good. The largest texture I managed to load was around 3GB (2048x2048x7**), but often it throws an error. Despite the fact that it should have a large amount of free VRAM that would fit the texture, it may fail to allocate such big chunk due to various reasons. So I would not recommend allocating textures that are comparable to the total size of VRAM unless it is absolutely necessary.