I asked the SSA staffer when I went to update after naturalizing, because they ordered a new one for me. I had received an unrestricted one after AOS, so I didn't need a new one. I was told if it was done as part of AOS or citizenship updates, it didn't count against the total.
Then again, being told this by a government employee means there is a good chance that it DOES count, so your caution is prudent.