Yes, once your stucco is cured, you can do that. The first 2 or 3 curing fires will not generate a lot of heat or smoke (and, of course, you will not feel much heat if any on the underlying stucco).
I’d suggest working on the front (face) first, while you are getting cooler fires and so that you can take advantage of the slowly increasing peak heat.
As a reminder, front bricks need to leave enough space in front of them for the door to be able to stand. If you’re “closing off,” this is where you want to add bricks on their sides, and if you’re finishing over that, you’ll want to use split faces for just that area in the interest of having enough space.
Hope this helps, Dave!