If I wanted to copy a low resolution texture onto a higher resolution texture and I used a Blit Command Encoder would it preform linear sampling on the texture while it stretched it?
Blit command encoders can't do that at all, let alone perform interpolation while doing so. All of the copy methods take only a single size parameter, which is the size in both the source and, implicitly, the destination of the region to copy. It can't resize.
To do what you want, you need to use a render command encoder and draw a quad which samples from the source texture and uses the destination texture as the render target (color attachment). At that point, you have control over sampling/interpolation via the fragment shader and the sampler object you use to sample from the source when determining the color of a fragment.