The term of art is "crash consistent," and any ACID database must preserve all committed state across events such as power loss. Such a database is correctly backed up when copying a simultaneous point in time snapshot across all involved volumes.
Not all databases are truly ACID. Lots of software relies on uncommitted database state. But we're talking about a solved problem here; if you require ACID behavior the means to achieve exactly that are available. Any exception to that statement, including hardware misfeatures or lack of two phase commit across databases, is equivalent to "incorrectly designed."
In a correctly designed system quiescing the database isn't necessary, but might still be used as a precaution or a performance optimization.