Can wearing contacts stop your eyes from getting watery when chopping onions?

Yes. The lenses can block the vapors from contacting your corneas. I have heard from patients after lasik that they noticed a big change when chopping onions since they are no longer wearing contacts.
It may make it worse. The chemicals released when cutting into onions can be absorbed by contact lenses. They will then retain the chemicals longer, causing the irritation to persist.