Board mount AC/DC converter design concerns
Does it really protect my digital circuit in case of Hazardous
  situations like lightening and others?


The data sheet says this about surges: -

EN55024, heavy industry level (surge L-N : 1KV), criteria A


And all that means is that the unit will survive a 1 kV surge when applied to the AC lines. It doesn't mean that a surge will not produce a knock-on transient of some form on the DC output so you need to take care of down-stream effects yourself. These days, surviving a 1 kV surge is old-hat and rather feeble so, you have to put things into context. If you can, try and find a device with better survival qualities - for instance, ethernet devices tend to be able to survive 6 kV.

However, the data sheet also says this: -

Protection type : Shut off o/p voltage, clamping by zener diode


And that likely means that the output DC voltage is fairly hard-limited to some upper value but there's no guarantee that your electronics can survive that upper value. For a 5 volt output power supply, the upper value is stated as being 6.75 volts - so, is your electronics capable of surviving that extreme?

You also need to consider that surges can produce a common-mode transient on the DC output and this may also cause your load a problem especially if your load is not galvanically isolated from earth.

Summary: It depends on your circuit!