Many students start with cursive and it works really well. For some it is a bit easier to write in cursive because the flowing nature of cursive vs manuscript. My kids learn cursive along side printing for hand writing. Some books use printing to practice tracing letters and others cursive, so my children did some of both throughout each day. As they have gotten older they have created their own mix of print and cursive which is how I also write. I told them they can choose how to write as long as it is nice and legible, but they need to learn how to read cursive because old documents are often in a form of cursive.
So yes, in my experience we have had no problem starting with cursive. 🙂