Prepare grill for two-zone fire over medium heat (350 degrees F to 450 degrees F). Preheat a 12-inch grill pan on cooking grates.
For vinaigrette, in large glass serving bowl whisk together lemon juice, olives, and thyme. Slowly drizzle and whisk in olive oil to emulsify. Season with salt and pepper. Set aside.
In large bowl combine sweet peppers, artichokes, 1/4 cup olive oil, and garlic. Set aside.
Drain and add wood chips to smoker box of gas grill, following manufacturer's instructions. Close grill lid. When wood begins to smoke, arrange peppers and artichokes in a single layer on grill pan (fire may flare briefly). Cook over direct medium heat for 10 to 12 minutes, turning occasionally until slightly charred and softened, keeping lid closed as much as possible. Wearing insulated mitts, transfer grill pan to heatproof surface. Combine grilled vegetables with vinaigrette. Set aside.
Meanwhile, in a large pot of boiling salted water, cook pasta according to package directions. Drain pasta; combine with vegetables and vinaigrette. Sprinkle cheese; toss to combine. Serve warm or at room temperature.