Is it possible to use PBZ series with floating output without connecting the COM terminal to the chassis terminal?

The output terminal should be connected to the chassis terminal and grounded.
If not, common-mode noise may cause output noise. (Note that the specifications state that the COM terminal should be connected to the chassis terminal.)
Additionally, if there is an insulation failure inside PBZ series, this grounding will help prevent electric shock.
Since the output terminal is isolated from the primary side, there should be no problem with a floating output. However, as mentioned above, the floating output is outside of the specifications.
For the details, read the user’s manual – chapter of Installation and Preparation – Connecting the Load – Connecting to the OUTPUT Terminals.