No, no thorns on blueberries! My grandfather used to do research on blueberries and taught us all about them. We had over a dozen bushes around the property growing up. My biggest concern in AZ would be the desert conditions. The prefer acidic soil (we always used pine straw mulch for them due to its acidity) but they also require quite a bit of water. Whenever we had a drought they would get sad looking and the berries shriveled up.
Most blackberries do have thorns; wild ones certainly do. We had them growing up and down the road, along fence lines and on the edges of trails throughout the woods. My arms were always literally covered in scratches from picking them, and then I would have to pull dozens out tiny thorns out of my hands. But I always picked them the fastest of all my siblings.