In all honesty, no, you should not use boiling water to make green tea. We've said a lot here about how tea is never wrong as long as it tastes good to you, but using lower temperature water for green teas is the hill we just might die on.
Have you ever sipped your cup of green tea and wondered why it's so bitter even though you didn't steep it very long? It's probably because the water you used was too hot. Green teas (especially Japanese green teas) are very sensitive to water temperature. In essence, using boiling water on green tea leaves "burns" the leaves, extracting all of the tannin and leaving you with a bitter cup with little aroma or nuance.
If you don't have a variable temperature kettle, not to worry! You can use a candy or meat thermometer and add cool water until your water gets to the correct temperature. Alternately, you can keep an eye on the water as it heats and pull it off just before the tiny bubbles start to leave the bottom of the pot. (This water will be about 170° F.)