Can autothrust keep the plane aligned with the runway during crabbing?
EDIT: I take your question as "when crabbing the aircraft for landing in strong crosswind, is the auto-thrust precise enough to maintain horizontal alignment with the extended runway centerline?"

No. Auto-thrust is not precise nor responsive enough for this capability. Furthermore, auto-thrust is not used in this manner. To track the extended runway centerline when the crosswind changes, the pilots would increase or decrease the crab angle using rudder inputs.

Let us for a moment consider using auto-thrust to track the centerline. As an example, imagine an aircraft landing on runway 36 (pointed North) with a strong crosswind blowing East to West. The plane's heading will be somewhere between 360 and 90 degrees, while its track is 360. Suddenly, the crosswind increases, and the plane experiences a deviation to its left.



The plane is drifting to its left because the velocity component in the East-West direction is nonzero. If this is countered by increasing engine power, the plane can, theoretically, increase its velocity component pointing towards the East and get back on track. The problem is, flying a plane is three-dimensional! If engine power is increased, airspeed will increase, lift will increase, and the plane will drift above the glide slope vertically.

The correct response is this case is to input right rudder. Staying on localizer and glide slope requires frequent, precise but small changes. The right tool for that is the control surfaces. When using the crab technique in a crosswind landing:


Elevator is used adjust the plane's vertical speed
Rudder is used to adjust the plane's crab angle
Ailerons are used to maintain the wings level (to counter the aircraft's tendency to bank when using rudder)
Thrust is used to maintain airspeed (which keeps the plane from stalling)




From your question, it appears that you may have some misconceptions.

Thrust is forward. It controls the airspeed, which is also related to the angle of attack. Crosswind is wind blowing either left-to-right or right-to-left. Therefore, thrust and crosswind are unrelated; auto-thrust will not compensate for crosswind because thrust can only make the plane go faster/slower or go up/down, but crosswind blows side to side.

If your question is whether the autopilot uses asymmetrical thrust to control the plane in these conditions, then the answer is no: thrust is not responsive enough to control a plane's attitude, asymmetrical thrust is only used in emergency situations when no other options are available.

My bet is you're asking about gusts and wind shear, which can be experienced as either a headwind, tailwind or crosswind, so it may affect an aircraft's airspeed. Wind shear is defined as a sudden change of wind speed and/or wind direction.

The calculated speed of a landing is called Vref. In a normal landing, the pilots usually input Vref+5 into the autopilot. In gusty conditions, the pilots may input Vref+10 into the autopilot. A less flap setting may also be selected, again for the purpose of flying the approach at a higher airspeed. A higher airspeed is desired because it increases the stall margin.


  When using the autothrottle, position command speed to VREF + 5 knots.
  Sufficient wind and gust protection is available with the autothrottle
  connected because the autothrottle is designed to adjust thrust
  rapidly when the airspeed drops below command speed while reducing
  thrust slowly when the airspeed exceeds command speed. In turbulence,
  the result is that average thrust is higher than necessary to maintain
  command speed. This results in an average speed exceeding command
  speed.
  
  If a manual landing is planned with the autothrottle connected
  in gusty or high wind conditions, consider positioning the command
  speed to VREF + 10 knots. This helps protect against a sudden loss of
  airspeed during the flare.


quote from Boeing 777 Flight Crew Training Manual

Auto-thrust itself is precise enough to handle gusty winds to an extent, but it has its limitations. IIRC using auto-thrust is recommended in these scenarios, as it reduces the pilots' workload in a challenging situation. Plane manufacturers and airline companies often have limitations regarding the maximum gust / maximum crosswind. Attempting a landing outside these limitations may exceed the auto-thrust's capability to respond to rapid airspeed changes; it may also exceed the landing gear's strength or the wing's loading and therefore is dangerous.