Spoon ice cream into crust; smooth top. Squeeze chocolate sauce in straight lines over pie, spacing 1/2 inch apart. Draw tip of knife through chocolate lines, forming chevron pattern. Sprinkle with almonds; freeze until firm. DO AHEAD Can be made 1 day ahead; keep frozen. Let pie soften slightly before serving.
Just before serving, bring all berries, 2 tablespoons water, and brown sugar to simmer in medium saucepan over medium-high heat. Cook until sauce thickens, stirring gently, about 4 minutes; remove from heat. Cut pie into wedges; place on plates. Spoon warm sauce over.