No, the brick is painted. I believe the brick used was a true old brick, hence the texture. The mortar joints were also left less refined and were not tooled. It's sort of a flush joint that is less clean because of the irregularities in the brick. Below is a closer photo of the brick on this home. You can see the inconsistency in the mortar joint better.

You should be able to show any skilled mason this photo and they should be able to reproduce that texture. I would also request a wall sample mock-up of the brick before they proceed.