Can I run a 2000W power tool off of a 2000 (4000W peak) modified wave inverter?
no.

Power tool motors typically want about 10 times their rated power to start.  4000W peak is probably nowhere near enough for a 2000W motor.

If the inverter is capable of enforcing the 4000W limit without shutting down it will probably work, (but saw will be slower to start)