Can You Damage Car's Alignment If You Hit Curve During Parallel Parking?

First of all... Wrong. Bumping the curb does not change the ballance but it will eventualy whack the alignment of the front wheels over time causing tire wear and poor handeling. The front and rear bearings are tough enough to withstand very heavy shock loads so no worrys there. Hitting a 3 inch bump in the freeway at 60MPH is more of a shock load then a curb bump at 2MPH.

Please tell me that you are not parallel parking at 30MPH.

The major issue is scratching the rims or damaging it sidewalls of the tire.

Yes, bumping a curb can affect your tire balance. You could very possibly pull off a wieght, dent the rim so now it spins different and needs to be re-balanced. The parts most likely to be damaged are the rims, tie rods, rac and pinion, tie rod ends, coil springs, struts. It can cause damage but typically a slight thump wont do anything. If you hit the curb hard enough to jolt you around, it could cause damager. Depending on how old the car is and how much corrosion the parts have will determine any damage.