The answer to your question is no. NW international K fares cannot be upgraded with any miles.

The rules for international upgrades are confusing, but boil down to the following:

• If using NW miles for international upgrades, you can only upgrade NW Y or B, KL S or B, or CO Y or H. No other classes can be upgraded with NW miles.
• If using CO miles for international upgrades, you can only upgrade NW Y o B, KL S or B, or CO Y or H without a co-pay. Other CO classes (like K) can be upgraded with CO miles + a co-pay.

Rules get a little more complex for code shares.