Being immutable, SSTables do help a lot when it comes to backups, indeed.
Your ideia sounds ok for situations where everything is healthy on your cluster. Actually, Cassandra is consistency-configurable (if I say eventually consistent, some people may be offended here, hehe), and as the system itself may no be fully consistent at a given time, you cannot say your backup will be as well. But, by the other hand, one of the beauties of Cassandra (and NoSQL models) is that it tends to recover pretty well, which is true for Cassandra in most situations (quite opposite to a relational databases, which are very sensitive to data losses). It's very unlikely you end up with a bunch of useless data if you have at least fully preserved SSTables files.
Be aware that EBS Snapshots are block-level. So, when you have a filesystem on top of it, it may be a concern as well. Fortunately, any modern filesystem have journaling nowadays and are pretty reliable, so that shouldn't be a problem, but having your data in a separate partition is a good practice, so the chances of someone else writing in it right after a full flush are smaller.
You may have some lost replicas when you eventually need to restore you cluster, demanding you to run nodetool repair, what, if you have done before, is a bit painful and takes very long for large amounts of data. (But, repair is recommended to be run regularly anyway, specially if you delete a lot.)
Another thing to consider are hinted handoffs (writes whose row owners are missing, but which are kept by other nodes until the owners come back). I don't know what happens with them when you flush, but I guess they're kept in memory and on commit logs only.
And, off course, do a full restore before you assume this will work in the future.
I don't have a large experience with Cassandra, but what I have heard about backup solutions for it are whole cluster replicas in another region, or datacenter, instead of cold backups like snapshots. It's probably more expensive but more reliable too than raw disks snapshots like you trying to do.