From what I can see, the PD4590 is a 13.6v converter. If it has the optional Charge Wizard, it becomes a 3 stage converter. Yours may or may not have the Charge Wizard.
If you have a voltmeter you can measure the output voltage of the converter. The Charge Wizard makes the converter put out 14.4v, 13.8v (I think) or 13.2v depending on the battery state of charge (SOC). Without the wizard it puts out 13.6v.
Yours may or may not be a smart converter and thus may not be as safe to leave connected.