Yes, the image position (0020,0032) coordinates are absolute coordinates. They are relative to an origin point called the "frame of reference". It doesn't matter where the frame of reference is, but for CT/MRI scanners you can think of it as a fixed point for that particular scanner, relative to the scanner table (the table moves the patient through the scanner, so the frame of reference has to move too - otherwise the z-coodinates wouldn't change!)
What's important when comparing two images is not where the frame of reference is, but whether the same frame of reference is being used. If they are from the same scanner then they probably will be, but the way to check is whether the Frame of Reference UID (0020,0052) is the same.
A few things to note: if you have a stack of 2D slices then the Image Position tag contains the coordinates of the CENTRE of the first voxel of the 2D SLICE (not the whole stack of slices). So it will be different for each slice.
Even if two orthogonal planes line up at an edge, the Image Position coordinates won't necessarily be the same because the voxel dimensions could be different, so the centre of the voxel on one plane isn't necessarily the same as the centre of the voxel on another plane.
Also, it's worth emphasising that the coordinates are relative in some way to the scanner, not to the patient. When your planes are all reconstructed from the same data then everything is consistent. But if two scans were taken at different times then the coordinates of patient features will not necessarily match up as the patient may have moved.