Does Modern Greek still use letters to indicate numbers?
From what I can tell, they still are using them when it comes to divide books or long essays in chapters. Normally one uses first the Roman numbers, than arabic ones for sub orders and last the ancient Greek numbers. Fro the Greek numbers the tendecy nowadays is to use them following strict the alphabet (e.g. ζ’ for 6 and not στ’), when the numbering does not exceed the nuber 24, otherwise they will use a mixed system of arabic numbers and greek letters, e.g. 1α, γ1. Only when it comes to numbering the verses of the bible Greek number system is used exactly as in the traditional ways.
Modern Greeks tend to use the Ancient Greek numerals as frequently as we use the Roman numerals. In my experience, they use the same confusing system as the ancients. 
hehe it’s not confusing really!
Anyway, the use of alphabetical order (“ζ” instead of “στ”) appears only in documents created in MSWord
We use ancient Greek numerals much more often than Roman (I guess because we always have to stop and count the Is and Xs ) but we use them too from time to time (just don’t ask most Greeks what M or C stands for)
Ancient Greek numerals maybe used in any kind of “list”