No. The Sims on Nintendo GameCube (released 2003) is a simplified port of the PC original. Due to hardware limitations and design choices, it omits the pregnancy and baby-raising mechanics entirely.
If you want generational gameplay, you need the PC/Mac versions (The Sims 1 with expansions, The Sims 2+) or later console entries like The Sims 2 (PS2/Xbox/GameCube) which reintroduced babies and aging.