I'm sure some of them would, but they're not required by law to do so. And historically the way you'd do this is by actual fragment/substring matches. But these are novel viruses now. So what you really want to do is try to predict whether a novel genome is pathogenic... which is itself obviously a very hard technical problem.

No, of course not. In 2010 I went to a guest lecture from a guy who worked on the scanning algorithm for IDT. A few years later, there was a minor scandal when someone in a nearby lab used a personal credit card for a purchase and got a big shared account locked. So not only were they scanning the content of synthesis orders, they were validating payment back to labs. In 2010, when HTTPS was rare and facebook didn't even offer it.