probably reasonably well, except for some poetry. There are some significant dialect shifts in (apologies, no greek IME installed on my phone ATM) katharevousa

probably reasonably well, except for some poetry. There are some significant dialect shifts in (apologies, no greek IME installed on my phone ATM) katharevousa vs standard dimotiki vs ancient koine (i.e. there is no tha' ), but I think quite a lot of the vocabulary has remained stable, in contrast to the tectonic shifts that taken place between Old English, middle english, early modern and Modern English. Greeks who go to church (assuming it's Greek Orthodox), are thereby exposed to a narrow corpus of Hellenistic Greek, which is a middle stage between the greek of homer and the modern version.