Yes, the stative endings look like a conjugation but they are unique to the stative which makes me wonder if this verb form may have been adopted from the Buto linguistic zone after unification.
The other interesting thing about the stative is that it was usually (unless wish or command) preposed by its subject, like the adverbial predicate construct and the subject-sdm.f construct. The latter two indicated imperfect aspect In Old Egyptian; "I was/am/shall be going". With the stative, however, you have a very interesting differentiation:
1) Intransitive verbs: Originally it marked completed action: I have gone. Semantically, "I'm gone" is the state resulting from this action once completed.
2) Transitive verbs: Completed action and resulting state have separate verb forms. IN Middle Egyptian, the sdmn.f took over the former (Allen's ex.: "I have entombed") and the stative took the latter ("I am entombed") as the language further differentiated and refined.
This suggests that the original stative expressed the verbal aspect of completion not merely resulting state, the later function. And so this might be a way to link it to another linguistic realm if the grammar has been sufficiently elucidated elsewhere.