Does the Airborne still blouse their boots in the current Service (Dress) Blue uniform?

Yes, DA PAM 670-1 para 20-3.

a) Only Soldiers authorized to wear the tan, green, or maroon berets, those assigned to Air Assault coded positions, and MPs performing MP duties may wear black combat boots with the service/dress uniforms. When worn, the trousers or slacks are bloused (tucked-in or by the use of blousing rubbers/bands). When trousers or slacks are bloused, personnel will not wrap them around the leg so tightly so as to present a pegged appearance. When the trousers or slacks are bloused properly, the bloused portion of the trousers or slacks should not extend below the third eyelet from the top of the boot. Soldiers will not blouse boots so that the bloused portion extends down to the ankle area of the boot.

We also bloused them in the 101st ABN (Air Assault).