It is possible to install a small block Chevy engine in a 2001 Toyota Corolla, but it would be a highly custom project requiring extensive modifications to the vehicle. The small block Chevy engine is much larger and heavier than the original 1.8-liter inline-four engine in the Corolla, so significant changes would need to be made to the engine bay, transmission, drivetrain, and suspension to accommodate the new powerplant. Additionally, the electrical system and engine management system would need to be modified or replaced to work with the Chevy engine.
Overall, installing a small block Chevy engine in a 2001 Toyota Corolla would be a complex and expensive undertaking, and it may not be practical or cost-effective compared to other options for modifying or upgrading the vehicle's performance.