Place chicken in a large resealable plastic bag set in a shallow dish. Pour dressing over chicken; seal bag. Chill for 30 minutes, turning once.
Drain chicken, discarding marinade. For a charcoal or gas grill, place chicken on the grill rack of a covered grill directly over medium heat. Grill for 12 to 15 minutes or until chicken is no longer pink (170 degrees F).
Meanwhile, in a medium bowl toss artichokes with oil. Preheat the grill wok alongside chicken on the rack of the covered grill over medium heat for 15 seconds. Add artichokes to the grill wok. Grill artichokes in wok about 10 minutes or until tender, stirring occasionally. Transfer chicken and artichokes to a platter; keep warm.
Cook pasta according to package directions. Drain; return pasta to saucepan. Stir in Alfredo sauce. If desired, stir in additional milk to reach desired consistency. Stir in artichokes, bacon, and parsley.