Archive nodes are only necessary if you're going to be querying historical nodes that are no longer on the state trie.
That said, even fast-pruned nodes allow you to inspect some (configurable) depth of history on the state trie, so whether it's sufficient depends on your use-case.
A cheat sheet: https://dev.to/5chdn/ethereum-node-configuration-modes-cheat-...
I can't speak to this specific chart but if you fast sync a Geth node the final result does include the state. So, I assume that this chart does include the state. It only includes the most recent state though.
For Geth v1.9.0, look here for some new details on sync time. Describes all three modes and times including some changes that one should know about.
As of Aug 2, 2019 the size on disk for me was 356 GB and state entries went to 370 million. Takes a couple of days to sync with a ssd drive. Be patient.