I don't think they would though. It's not TE that refuses the visa when somebody has had overstay. It's immigration themselves that check the system before inserting the visa.
It's weird that even during the application, any overstay doesn't appear to be checked.
Thats why TE state in the t&C that if you don't tell them when you apply, immigration will pick it up on the day you go to get the visa.
You should be ok for the first entry and 1st year with that particular insurance. If it will work for subsequent entrys or for the second year entry, I'm not sure. I don't believe they are on the list of insurers for extensions, so it wouldn't work for that purpose.
Not really seeing any posts of O-A visas issued after 31st October and using non listed Thai insurance to know how it may play out.