Can I open a Thai bank account with a work visa from teaching?

If you have a Bachelors degree (legal requirement in Thailand) and you fall within their preferred age range you may get a teaching position and a Non B visa and the school usually has a bank they prefer to do business with. They will usually assist you in opening the account. Having the Non B visa and work permit will usually make it easier to open a bank account at whatever bank you choose as well as getting a post paid SIM card with the phone provider of your choice.

You will most likely qualify for a bank account especially if your school sponsors your visa. In my personal experience, my wife and I taught in Bangkok and we had our bank accounts opened at Bangkok Bank. We were lucky enough to get them opened before our permits. But I’ve found it does depend on the relationship between the school and the bank.

There's nothing that "qualifies" you for a Thai bank account. There is no visa or visa type that does or does not legally allow a bank account. You will need to find a bank willing to open an account for you.