Your primary question, if a linear actuator can be moved with the power off, will be no, unless you find a mechanism specifically created for that purpose.
These actuators are effectively a pinion gear design with a very high reduction ratio. You'll note in the link you provided that heavy lift mechanisms such as a motorcycle lift and a medical bed are presented for this type of use. They work well because you can position the bed/lift top where you wish and stop without additional locking mechanisms, although you'll find most have a safety latch of some sort.
For your application, closing a door, this type of linear actuator will be poorly suited.
I can envision a more mechanically complex arrangement which would use a linear actuator. Consider the manual release for a garage door opener. The chain and carrier for the opener can be considered the linear actuator.
If I disengage the manual release, then activate the button or remote, the door will remain closed. I can open and close manually the garage door without interference from the motorized mechanism, as long as I do not engage the latch system that is part of this garage door device.
If the linear actuator in fully-open mode has a pusher block attached, and remains in open mode, your door will operate normally. A sensor tells your system that the door is closed after the appropriate period.
If not, the device actuates the actuator and pushes the door closed, until the sensor informs the device that it is closed, at which point, the actuator returns to the original location, ready to push again on command.
There may be other approaches using clutches, cables, etc., but this is the one that popped into my alleged mind as an option.
EDIT: similar method to my suggestion, based on new information regarding the placement.
Consider that the actuator is on the inside of the door, as specified. When idle (door closed), the actuator is retracted, to a point where the end of the ram is not in contact with the door.
At the end of the ram is a magnet of sufficient strength, matching placement on the door of a metal panel.
After the door is ajar for the specified time, the ram/actuator will travel to the limit, "collecting" the door in the process. If that aspect is undesirable, a limit switch could be placed on the actuator, triggering motor reversal. Simple microswitches such as those used in 3D printers are inexpensive and easily found online.
When the actuator contacts the door, either at full travel or with the switch activated, the magnet will pull the door closed as the ram retracts. When the door is closed, the additional space between the ram and the door will disengage the door, returning it to normal service.
If magnets are not desirable, a more complex design using the limit switch concept to trigger a latch and socket mechanism could be implemented. Additionally, a low-to-medium force detent mechanism might work, but that would require full extension to engage. Think of a horizontal plate on the door with a large diameter hole in the surface. The end of the ram would have a sphere that has to deflect or be deflected in order to engage the hole. Once engaged, reversal will pull the door closed until the retraction force pops the sphere free from the hole. Less reliable, less fussy to build, but still an option.