Kind of. It's more like they can sense when something bad is going to happen, like rats do when they seem to randomly jump off a ship, and the next thing you know it's sinking. They wouldn't know exactly what specifically is going to happen. The way I imagine it, nature kind of talks to itself. The Zanarans by this point are already looking for Aran, and using a great deal of magic to do it. Magic has a certain effect on nature, so "word" gets around.
At one point in the story, Lyndsey is being chased by something and a plant saves her life by flashing a picture of flame into her head when danger is coming closer, so she knows where not to run.
So not really. They can't technically tell the future, but they can warn people who are receptive, like Lyndsey, that something is coming.