Blend 1 1/4 cups cilantro leaves and next 4 ingredients in processor until coarse puree forms. With machine running, gradually add 1/2 cup oil. Season generously with salt. (Pesto can be made 1 day ahead. Cover and chill).
Cook linguine in large pot of boiling salted water until tender, but still firm to bite, stirring occasionally. Drain.
Meanwhile, heat remaining 1 Tb oil in heavy large skillet over medium-high heat. Add shrimp and cook until almost opaque in center, about 3 minutes. Remove skillet from heat; add tequila. Return skillet to heat and stir until sauce is syrupy, about 30 seconds. Add pesto; stir to coat. Remove from heat.
Add pasta to sauce in skillet; toss to coat. Season with salt and pepper. Divide pasta and shrimp among 4 plates. Sprinkle Cotija cheese and chopped cilantro over and serve.