I can't specifically answer for a SSD, but in the Datejust they are interchangeable. So. I would assume they are. The most important thing is making sure you get the movement with tall hand pins. If you get the wrong size and have to change them from the old movement, it's definitely a job for a watch smith, not an amateur. The standard size won't work.
And don't worry about the day wheel. It doesn't show with the dial in place.