Short answer: it really depends on the kind of application you are running on your instance.
Long answer: Basically, taking an unquiesced snapshot of a running machine is similar to "pull the power plug" - ie: a sudden, immediate, unexpected crash.
When running with I/O barrier enabled, modern journaled filesystem should be consistent in spite of any crash. This does not means that in-memory data will not be lost; rather, that commited data are guaranteed to be stored on persistent storage (ie: disk).
This really applies to any properly journaled application, especially ACID-compliant databases (a non inclusive list: MSSQL, InnoDB, PostgreSQL, Oracle, IBM DB2, ecc). Again, this does not means that a sudden power loss (or a restored, not-quiesced snapshot) will not lead to any data loss; rather, it means that when a (possibly implicit) COMMIT returns, any relevant data are on stable storage.
With such journaled application, you don't strictly need to quiesce the filesystem. The first boot after a restored snapshot, the system will reply its journals (filesystem and databases) and a consistent state will be reached.
However, there are many applications that do not properly journal their updates, and which require the equivalent of a
fsck to return to a consistent state. The main example is MySQL+MyISAM: this (very common) database engine is not ACID compliant, as its great write speed is achieved by batching unrelated I/O operation with small regard for regular I/O barriers. An unproperly shutdown (ie: power loss, system or mysql crash, unquiesced snapshot) MyISAM database can be inoperable until a
mysqlcheck/mysqlrepair is performed.
The various guide recommending to quiesce the filesystem before a snapshot do that for this exact reason: some "unprepared" application (read: MyISAM) can be somewhat damaged by the sudden shutdown and subsequent restore, requiring a consistency check.
Bottom line: if you use a journaled filesystem with enabled I/O barriers (default on ext4 and XFS) and an ACID-compliant database, you should be safe taking unquiesced snapshots. At worst you can see some non-fatal error/warning when mounting the snapshot, but journal reply will bring the system in a consistent state. If using MyISAM, however, it is better to freeze/quiesce your filesystem before taking a snapshot.