Is the modern pronunciation of Greek accurate for koine?

It’s close. This is from memory, so I could be wrong in a couple of details. 1st century AD Koine was the same as Modern Greek in the following:

• Stress accent, not pitch accent
• Diphthongs pronounced as single vowels
• Most vowels with modern values
• Most consonants with modern values
• No aspiration

It differs as follows:

• Upsilon and Omicron iota pronounced as /y/.
• Eta still /ɛ/,
• Phi in transition from /pʰ/ to /f/ via /ɸ/.
• Beta is /β/, on the way to /v/
• According to Wikipedia, delta and gamma were already /ð, ɣ/. I remember /ð/ being as late  as 4th century AD, but what the hey.

See Koine Greek phonology 

In summary, if we go by the Wikipedia article for popular Greek pronunciation, the only letters whose pronunciation was substantially different  from Modern were eta, upsilon, and omicron iota.