Sure, it is okay to piece the stashing. I do it all the time. As I keep reading here, there are no quilting rules.
I haven't heard an opinion on alternating the seems or keeping them in the same place. I will be interested in seeing what others say. It may just be personal taste.
I look forward to seeing a picture of your quilt. (It doesn't have to be finished to show it off, you know.)
Dina