Yes and no. I am not saying that BT is unprotected, but at the same time they do NOT expect an attack like the Seanchan would do. The Asha'man do not know how to block gateways from opening, so the best the wards would do would be to warn them that someone is channeling saidar inside the tower.

They also do not expect an attack via traveling since they think the Seanchan don't have that. Aes Sedai do, but the oath against killing prevents the AS from performing an all out ambush attack like the one I am thinking off.

Here is a theoretical possibility:
Lets say the attack happens during the night as I originally suggested, there are likely guards, but most of the Asha'man are sleeping. Suddenly 25 gateways open all over the BT area. And out of each gateway two damane/sul'dam pairs run through and INSTANTLY start using the OP to throw fire and destruction at the best of their ability. What do you think would happen? I would say that a lot of people in BT would simply die before they even knew what was happening, while the rest would take a while to react and start fighting back, during which time even more would die.

BT might not fall from an attack like this, but they would likely take very heavy casualties. One might even say that the Black Tower would be rent in blood and fire. And would that not be basically what the Seanchan want? Unlike with the AS and WT, they don't want to capture the Asha'man, but rather to kill them all as quickly as possible.