Modern Greek is enormously helpful as an aid in making Koine "active." It is very close to Koine, basically, a simplified version. While I do not believe the pronunciation of Koine was exactly the same as Modern, I believe it was actually pretty close. I also believe the rhythm of the two dialects is probably very similar. Additionally, there is a HUGE vocabulary overlap.
For all these reasons, learning Modern Greek is probably the best thing one can do to take their Koine to a much higher level.
If anyone is interested, there is an excellent free Modern Greek course, which goes all the way to the Advanced level, here:
http://www.kypros.org/LearnGreek/
Another interesting comparison is to take the Greek New Testament and compare it to one of the Modern Greek translations of the New Testament (e.g., Μετάφραση Σπύρου Φίλου Metaphrase Spurou Philou). That will allow you to compare the two dialects side-by-side using a common text.
If anyone has further questions, please feel free to email me at: egwpisteuw@gmail.com.
