Can you go blind from having watery eyes while chopping onions for a salad?

Just tearing. The aroma of onion is irritating to your eyes and causes you to tear - but there is no danger of injury to your eye or damage to your vision.
No. The chemicals given off by the onion are an irritant, which causes watery eyes but in the normal course of cooking, even if you are a chef, there is not so much irritation so as to cause blindness.

Related Questions

Can you go blind from having watery eyes when chopping onions?

No. It's reflexive tearing, and steps can be taken to avoid this. Read more...
No. Onions release sulfa compounds when cut which vaporize and enter the eye tears as mild sulfuric acid. This is irritative and painful but causes no permanent harm. Most cookbooks have methods to minimize this but it is an occupational hazard of cooks. Read more...