There are a few spots nestled away in a corner on the wall where an arrow cart and operator are safe but can still pummel the gate in the south towers. In general the walls in EB are pretty safe for arrow carts (except quentin if you get a group with a ballista who knows what they're doing). You might take a few meteor shower hits in the south borderlands towers but other than that you're fine.
You have to watch for two things when trying this, one is your sage health. The other is your own. Dependant on where either of them are one or the other gets owned.
You still have to contend with the catapult against the gate. It will tear apart any rams you put up. It gets better if the defenders put the arrow carts behind the gate too cause they can still shoot past the gate or at it.
If rams are put up properly they get just splash damage which isn't too bad. Definitely the cart thing on the other side though.
Catapults don't have to be exclusively used on walls. If the keep you're attacking has upgraded walls but not upgraded gate you can still use the catas on the gate.
The basic point is that the cata against the gate thing can be countered and quite easily. Just spend 12 more silver on your siege plan, get catapults, and have the option to go through a wall if the gate is a death trap. Save your rams for when the keep is completely undefended.