Right, the crosswind accelerates a bullet sideways. If the bullet actually kept up with the crosswind, a 10 mph (14.667 fps) crosswind would displace that .17HMR bullet 57 inches instead of 17 inches during the .324 seconds it took that bullet to go 200 yards.
How 'late' a bullet is getting to the target is called the lag time and the moving shooter and target in a calm situation I detailed shows why wind drift is proportional to lag time, not time of flight.
That 220 grain .30 caliber bullet with a muzzle velocity of only 1040 fps took nearly twice a long to reach the target, yet it drifted a whole lot less than that .17 caliber bullet.
BTW, the drifts that my "moving target and shooter" model estimated agree with the wind drifts that ballistics calculators spit out in case no body got that.