The way Spine currently works, it renders the viewport to a very high resolution (whatever your window is sized to), so even with linear filtering off, all pixel animation lerps things at fractions of a pixel, and while the animation might look smooth in Spine, it could be janky in a pixel art game where the res is very low (for example 480 x 272). For example a subtle breathing motion where a character's chest sprite moves up and down from y = 10 to y=9 and back would look smooth in Spine but in game it would be harshly popping between two positions. As far as I can tell, there is no way get get spine to render things this way itself.
One of the things I do in AV is render the whole thing to a 480x272 target, clamp images to the nearest pixel when they're rendered, then render that to a stretched out HD target . So internally sprites might have a position of 5.5, -0.5, but it outputs them to the screen at 6,-1, then the final image gets a 4x treatment so they appear at 24,-4.
I think it would be helpful to have a "Pixel Resolution" feature for Spine to do all of its rendering at a low resolution, clamping output translation of images to pixels, only scaling them up to screen size as a last step.