Correct.
But it depends. A lot on jurisdiction and local law.
Most banking systems I've worked with have a field 'cheque book issued' which is sometimes linked to a rule 'cheques outstanding'.
If the 'cheque book issued' field is false, no kind of cheque will be cleared. I'm not familiar with the US, but if an account was named a 'chequeing accound' would imply this is always set to true. Various red flags also exist, as a cheque book has cheques numbered, so the same number being used would result in payment denied. In the UK, payee blank cheques were disallowed in the 1990s, etc.
A long list of red flags, because banks hate cheques. The industry term is 'Manually Initiated Fund Transfer' which means, at some part of the transaction (any transaction - could be updating an interest rate, or an authorised signer), a manual step was involved. This creates huge risk of fraud, banks dislike fraud, and legal punishments are large, especially for the bank which has a procedure with holes to let it happen.
Cheques are manual, the responsibility is on the bank. An online initiated transfer, the responsibility is on the customer to ensure their password is safe (and the bank to also do automated checks - unusual IPs, 2nd factor confirmation, but much easier to automate). So a bank refusing to authorise payment from a cheque written on a napkin can be expected, as long as the process is documented as fraud control. Printing on company-headed document would probably work - the first small payment would raise many red flags, but if that cleared, future similar payments would be OK'd.
A single cheque to empty an account? Some kind of 2nd factor authentication would be employed by any sane bank, such as an old-fashioned call to the number the account is registered with.