Yes! It happens in every main series games from Generation 3 (I only know about that). When you send out a Pokémon in a battle with full health, it has it's normal cry. But when it faints, it's pitch gets deepened and cry becomes lengthier! A Pokémon cry began to worsen when the HP indicator turns yellow colour. This gets even more bad as the gauge lowers!
Thank you!
Source: my experience.