The maximum recommended dose of aspirin is less than 4 grams (4000 mg) per day, and less than 100 grams at a time. So, yes, it would take a lot of those little tablets to kill you, though you might hurt your stomach if you swallowed a fistful.

Why are you asking? If you think someone may have taken more than 20 of these pills at one time, get them medical attention.