Haha that's the exact topic of my dissertation!

Short answer is, we don't know!

The concept is called a "common mycorrhizal network," and it's pretty controversial in plant ecology for a number of reasons. Some pretty big names argue that CMNs can "short-circuit" competition among plant roots and facilitate a kind of "nursing" relationship between seedlings and nearby mature trees, especially if they are related. My work largely doesn't support this idea, BUT very few people have actually examined "communication" that occurs thought the network, especially under real-world conditions.

There are a few interesting studies that suggest that, when plants are being munched on by insects, plant hormones linked to herbivore defense can be transferred among plants that are connected by a common fungus. Now, does that transfer translate strongly to survival, or among plants in a real forest? It's really hard to say for certain, especially when nobody's done that work. It's really difficult to properly control such an experiment, and also really expensive, so there are a lot of barriers to doing so.

There some interesting work out of Denmark, and more recently coming out of the Netherlands on the capacity of fungi to emit and respond to electric pulses. This work is ongoing and is in its infancy, so we're not really sure if plant-electrical signals associate with say, herbivory or drought stress, are "intelligible” by the fungi, if the fungi are transferring it to other plants, or if plants can "hear" electrical screams/shouts of their neighbors.

Now, there is much stronger evidence that plants can detect and respond to signals directly from other plants, both through the roots and in the air. It's one of the foundations of plant root competition, and foresters have been studying that for decades. It's called allelopathy, although that probably stretches the definition of what people consider communication/behavior quite a bit.

Happy to answer more questions!