Esper Sojourners

If you cycle this card, the cycling ability goes on the stack, then the triggered ability goes on the stack on top of it. The triggered ability will resolve before you draw a card from the cycling ability.

You can cycle this card even if there are no targets for the triggered ability. That's because the cycling ability itself has no targets.

The cycling ability and the triggered ability are separate. If the triggered ability doesn't resolve (due to being countered with Stifle, for example, or if all its targets have become illegal), the cycling ability will still resolve and you'll draw a card.