Unlikely.
It's worth remembering that Jones was never actually tried for defamation. He instead received a default judgment. In the US, both sides of a civil case have the right to a fair and speedy trial. If there's delays, you had better have a good reason for them and they need to fit the rules of procedure.
Jones and his company, Free Speech Systems, more-or-less refused to participate in the trial. The Knowledge Fight podcast has some episodes dealing with the discovery and deposition process for the suits, with actual deposition audio. I'm not a lawyer but it was absolutely brutal to listen to how ill-prepared Jones, his employees, and his representatives were. They were submitting Wikipedia articles about false flags as evidence, had a comprehensive background check on one of the parents that was in FSS records that no one could seem to explain the presence of, and generally didn't comply with other discovery requests.
The end result of this is that his life's work has been reduced to a satire and he is likely financially hobbled for the rest of his life.
For The Onion to have the same fate, they would have to basically disregard every single common-sense rule regarding what you should do when you're sued.