In theory yes, but in practice no. I have seen even 1 day insurance getting approved. But suggest for people to take 15 or 30 days, especially if they are only taking Thai insurance as back-up for their own insurance.
Having said that any health or travel insurance will be accepted.
Your Allianz is okay for TP. They do no longer reject for not mentioning amounts, nor Covid-19. All (foreign) insurances nowadays have higher coverage than the Thai requirements.
Need to attach cover page with name and policy number, mentioning medical treatment coverage.
You can apply with it immediately to see.
In case of a rejection for whatever reason: buy FWD. Don't bother about the 14 days waiting time. It will be accepted as is.
(Note: There are a few insurances that explicitly exclude covid. You cannot use these.)