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).

Yes they do.

I certainly hope that Airborne soldiers blouse their boots in the current Dress Blue uniform 1stSgt (Join to see)
Per current regulation Airborne including Ranger and Special Forces are still authorized to blouse their boots with the new dress uniform. Army Pamphlet 670-1
b. Boots, combat: black, leather. The black combat boots are an optional purchase item.
(1) Description. The black boot is made of black leather with a deep lug tread sole made of vulcanized rubber, a removable cushioned insert, a closed-loop speed lace system, and a leather padded collar.
(2) How worn.
(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.
(b) The boots are laced diagonally with black laces, with the excess lace tucked into the top of the boot under the bloused trousers or slacks, or wrapped around the top of the boot. Metal cleats and side tabs are not authorized for wear except by honor guards and ceremonial units in the performance of ceremonial duties. When metal cleats and side tabs are authorized for wear, commanders will furnish them to Soldiers at no cost. Sewn-in or laced-in zipper inserts are not authorized.
(c) A vulcanized rubber sole is the only outsole material that currently meets the need for durability and traction on surfaces. Other materials (that may be of a lighter weight) may have significant problems in these areas.

That looks horrible

Yup