Is it possible to craft armor-piercing ammo while on the reloading bench?

Depends on the ammo type you want to create. For instance, you can't produce any of the specialty 9mm ammo yourself - it all has to be bought from vendors.

Specialty Ammo can be produced in the following varieties:

• .308, JSP Hand Load - Increased damage.
• .357 Magnum, JFP Hand Load - Increased damage, armor penetration, and reduced spread.
• .45-70 Government, SWC Hand Load - Increased damage, huge armor penetration.
• .50 MG Match Hand Load - Increased damage, reduced spread.
• 10mm, JHP Hand Load - Increased damage, at the cost of increased target Armor.
• 12 Ga. Coin Shot - A cheaper variant of Buckshot.
• 12 Ga. Slug, 20 Ga. Slug - Reduced Spread.
• 12 Ga. Magnum, 20 Ga. Magnum - Increased damage.

Additionally, all Energy Weapon cells (Energy Cell, Microfusion Cell, and Electron Charge Packs), can be produced in both Over Charge and Max Charge varieties for increased damage.

Note: many of these ammunition types, in addition to doing increased damage, will cause the durability of your gun to decay substantially faster. Use only as needed, and with caution!