Is it good to study modern Greek while learning Koine Greek?

I wouldn’t go so far as saying it would impede it, but you need to be careful. There will be false friends: words changed meaning from Koine to Modern. The drastic simplification of the grammar in Modern Greek will make you annoyed about having to learn more paradigms in Koine. I think, in many ways—particularly learning grammar and syntax, Modern Greek will be a distraction.

I can think of two high-level benefits, though:

• If you’re coming to Koine already knowing Classical Greek, Modern Greek is a very useful antidote: it reminds you that Koine wasn’t a corruption of the ancient language, but an evolution whose endpoint you can see in the Modern. (Robertson’s exceedingly chatty grammar of New Testament Greek appeals to Modern Greek a lot.)
• And: Modern Greek is a living language. So was Koine, and so was Ancient Greek, but because they’re not living now, Modern Greek can help remind you that Koine, too, was a language spoken by real human beings, who walked the earth on two legs.