So far the only weave seek act indepedently of the channeler was woven by Rand with Callandor to kill Shadowspawn and considering he indicated that he felt them dying it's possible that it was only somewhat independent of him.

We know that much simpler wards like what Rahvin and Sammael used would do an efficient job of notification. Also let's be reasonable no significant troop movement would be done using normal size gateways. Circles like the one used to move the rebels would be used and likely a circle would be used to monitor the wards.

Besides the issue of complexity there is also the simple fact that an automatic weave would block your own Travelers as well as your enemies. With a monitored weave allies could announce themselves like Graendal muses in her meeting with Moggy and Cyndane(don't we know a platinum blond named Cindy aka suzzane summers) The weave you suggest would be impractical.