Depends what the definition of 'need' is, you do not need to speek Greek to exist in Cyprus. i understand that in Paphos, Greek Cypriots equal foreigners 1 to 1 and as such English as a common language is dominant and without doubt is language number one in the local hospitality trade. I've met plenty of Cypriots 'in the family' that only seem to start to speak English when I speak Greek to them but they do speak English regardless of generation so 'feigning' lack of understanding due to shyness is common for those that don't speak English everyday !
Before moving out here i seem to remember that 'we' as Brits hated the foreigners not speaking English in 'our' country so I`m sure the Cypriots have the same feeling but its a regular every-day one that just maintains the barrier between the Brits and the Cypriots, one that is built from birth due to the last 50 years history in Cyprus.
Unless you are living right out in the far remote sticks the chances are nearly everyone you meet will speak better English than your Greek so be prepared to be put out when you ask in broken grammatically incorrect Greek and are answered in excellent, if accented English.
Once your Greek improves and the replies are rambling Greek then you know you are moving forward
, best way to learn any language is to be immersed in it after some sort of foundation but English is too common in Cyprus for that immersion to exist from day 1.