Yes, Sasainn and Sasannach come from Saxon (through Middle Irish Saxa, Saxain).
Also the name of the English language: Beurla comes from older Sacs-Bhéarla meaning ‘Saxon speech’ from Old Irish bélrae – ‘speech, language’, related to beul ‘mouth’.
Celtic languages use the name of Saxons to call England and related concepts, unlike the rest of world which used the names of Angles (cf. Welsh Sais ‘Englishman’, Saesneg ‘English’ or Cornish Pow Sows ‘England’, lit. ‘country of Saxons’).