My advice is simple. Get your friend to register. Otherwise your friend will get fined and will bring a bad start to your stay there when they have to cough up a fine of 2000 baht and his/her name on their list which if they do this again the fine gets bigger.
All it takes is one person to snitch and an immigration officer may just decide to turn up.
You need to look at your policy wording. It needs to state the coverage amount of your policy, cover while in Quarantine and also states clearly it covers covid.
Revolut has this in their premium and metal plans.