Does modern Greek use initials and/or initialisms? Like similarly to how we might call John Kennedy John F. Kennedy or JFK, or the Federal Bureau of Investigation the FBI.
Yes. See this picture of the signature of Nikos Kazantzakis (Νίκος Καζαντζάκης) from Wikipedia:
Yes. The Value Added Tax is /fipia/ (foros prostiθemenis aksias). The Communist Party of Greece is /kukue/ (komunistiko koma elaðas).
Notably, initialisms in Greek often use the "informal" alphabet used in early schooling for spelling out words, where vowel letters are pronounced as phonemes, and letters as the letter followed by /u/ or /i/, rather than the official letter names: /fipia/, not /fi pi alfa/, /kukue/ alongside /kapa kapa epsilon/.
Greek does not pronounce initialisms for proper names (that I know of), although initials do show up; ΓΑΠ for George (son of) Andreas Papandreou.