If a player defeats a monster on an Adventure Card, but fails the adventure, can the player still collect the monster token?

Sure thing! The only rule to remember when defeating monsters is that trophies are collected at the end of the resolution phase, i.e., upon completing or failing the adventure (important in case the defeated monster is a Mi-go, for example)

Yep. Despite the fact that doing so will fail the adventure and incur a penalty, going after and clearing off the monsters is a good strategy to make an adventure less difficult.