No. And No.
No matter what you may read, a sandgrouse (genus: Pterocles) does not nest with pigeons in the large reptile tree (LRT, 1235 taxa), but with the screamer, Anhima. And those two do not nest with Tetrao tretix, the black grouse, which nests between chickens and sparrows in the LRT.
Pterocles exustus (Temminck 1815) is the extant chestnut-bellied sandgrouse. This vegetarian prefers bushy, arid lands.
Timminck CJ 1825. Atlas des oiseaux d’Europe, pour servir de complément au Manuel d’ornithologie de M. Temminck. Belin, Paris 1826–42.