I found knowledge of Classical Greek a little helpful in reading modern Greek, though much more at the level of signs rather than newspapers, but almost entirely useless in understanding spoken Greek, since the sounds represented by the letters have shifted so much eg b->v, d->th, nt->d etc. For example, Odysseus (which of course is pronounced differently anyway in Classical Greek than in modern English) comes out in modern Greek sounding something like "Otheesefs".