Hi Cubibobi,
Practicing mindfulness of death is commonly taken to mean being aware and mindful that one will die for certain, and that one doesn’t know when this time will come. Being aware or mindful of this by itself, will not lead one to the sotapanna stage. I guess every human being knows that he will die one day and that too is being mindful to a certain degree.
However mindfulness of death in Buddha Dhamma refers to being mindful that one may die anytime and therefore striving to attain a magga pala or to a attain arahanthhood, without procrastinating. This is explained in maranasati sutta’s; https://suttacentral.net/an6.19/en/thanissaro
Even from the reference of the Dhammapada you provided it can be deduced that practicing the mindfulness of death by itself will not directly lead to the sotapanna stage.
“This girl from the day when she heard my exposition of the doctrine has practised reflection on death for three years. I will now go there and ask the girl four questions; and when she explains them I will express approval at each of the four points, and will utter the verse. By means of the verse she will be established in the fruit of the First Path (entering the stream), and through her the teaching will be profitable to many.”
Here it can be seen that it is after hearing the dhamma that the girl will attain the sotapanna stage.