Place the first five ingredients in a blender; if desired, add pepper sauce. Cover and process until blended.
Cut peppers lengthwise in half; remove seeds. Cut eggplant lengthwise into 1/2-in.-thick slices. Cut zucchini and yellow squash lengthwise into quarters. Place all vegetables in a large bowl; drizzle with 1/2 cup of the sauce and toss to coat.
Place vegetables on a greased grill rack. Grill, covered, over medium heat 8-10 minutes or until tender and lightly charred, turning once. Cool slightly. Reduce grill temperature to medium-low heat.
Cut vegetables into bite-size pieces. Toss with additional 1/4 cup sauce; keep warm.
Grill sausages, covered, over medium-low heat 15-20 minutes or until a thermometer reads 160° for sausages (165° for sausages), turning occasionally. Remove sausages from grill; toss with remaining sauce. Serve with vegetables.