Array textures do not contain textures; they are a single texture that contains a number of images, with each image being of the same size, format, mipmap depth, etc.
As such, the sampling parameters that are part of the texture apply to sample fetches for all images within the texture.
That having been said:
In the shader I perform a manual GL_NEAREST lookup via textureFetch().
This means your FS knows when to look the texture up with linear filtering and when not to. As such, you could have two different array texture samplers in the shader, one of which you expect to use linear sampling and one which uses nearest.
Both of these samplers can be using the same texture object, just paired with a different sampler object (which contains all of the filtering parameters for the texture). One sampler would use nearest filtering, the other would use linear.