The licensed runway starts at the threshold markings, so for public transport or anything else requiring a licensed airfield you must abide by it.
As has been stated above, for a private flight, be it in a 747, a business jet or a piper cub you can do what you want with the landowners permission...the portion of the runway is no diffent to a farmers field.
The displaced threshold is probably there for a good reason, such as not annoying the neighbours, so normally if the airfield operator wants you to comply with it you would, unless they give you permission to do otherwise.