Yes, they can. But the flowers are better.

Going one step further, you can gather the leafless stems into a bundle and roll it between your palms to release scent. We do this with stems of the lavandin "Provence" after we remove the flowers for sachets.

I am happy to see this question. I am in zone 6, had only a few flowers this year, but lots of green. Please, should I cut the lavendar at the base and hang upside down? I have a dry basement, dark, but somewhat warm. Would this be a good spot? I love the scent of lavender!

Cut stems as long as you like, but don't remove more than one-third of the entire growth at any one time. I have visions of you cutting the plant right down to soil level - more like nightmares, really! As long as there is good air circulation, they'll dry in your basement.