Shrewd Hatchling, -1/-1 Counters, Infect, Wither

[Path93]

{Shrewd hatchling} enters the battlefield with four -1/-1 counters on it, and its ability allows it to take a -1/-1 counter off itself whenever a red or blue spell is cast. If shrewd hatchling is poisoned, would its ability allow it to take off a poison -1/-1 counter when its ability is activated?