I've been doing this for years. In fact, that's how I eat rosemary. I bring in a cutting, eat off the lower part of it, make some slits on that "stem" part, wait a few weeks, then plant them. I also eat any part of the stem that looks densely populated with needles. When it goes out to grow, it won't have thick roots, so it's better to have sparse needles that need to be fed. I make the slit so that the roots can come out. I was taught that in a propagation
class and it works.
I find that they don't always create roots. Sometimes it's because the part of the plant that I cut off wasn't really that healthy to begin with. My wife thinks it has to do with the time of the year, but I surprised her this month by that. Since about 50% clearly have healthy roots, I have grown many new plants around the garden in the last few years. Works for me, but I'm open to anyone unveiling any new mysteries for me.
John S
PDX OR