One could say whatever one wants but I think that in this case it’s actually a conjunction and I doubt anybody has ever said “I per se I” (Edited to add: actually that makes sense - for the letter i - but in a different context: spelling and not alphabet recitation. “c, a, r : car”, “i : I”. _letter_ (per se) : _word_)
https://www.englishclub.com/efl/podcasts/interesting-facts/a...
At the end of the alphabet, students would say “X,Y,Z and, per se, & (and)”.