Spaghettification is completely independent of relativistic effects; it just has to do with the gravitational gradient near a very massive body. An object near a massive body experiences more gravity on its “near end” than its “far end” which causes a stretching force. This does mean that spaghettification would be noticeable, and likely very uncomfortable as you’re ripped apart by extreme forces.
You’d notice if it happened on/near your retina, it was very dark, and you were paying attention. Other than that I don’t think you’re going to notice.