[NOTE: I do know what happened IN GAME, Ness and friends return as heroes but technically that should not have happened]
Okay this is NOT the Giygas Fetus Abortion thing… I actually like how the developers used very strong symbolism to bring up such a dark concept that would fly over most...
I don’t think so.
Giygas and Giegue, while the same individual biologically, are from different points in time. Giygas going to (and being defeated in) the distant past does not erase Giegue’s childhood, exploits, and defeat - if they were, for example, to exist in the same time period, they would exist as separate beings. Otherwise, Giegue would not be able to be defeated and later become Giygas, and thus would not be able to go to the distant past and be defeated by Ness and co., etc.
In other words, biological time is separate from chronological time. Giygas was traveling trough chronological time, not his own biological time (like, say, if Giygas’s present consciousness went back in time and was being projected through his past body, a la Quantum Leap).