The short answer is yes. But such a mesh does not provide protection against direct lightning strike!
Any lightning rod is effective only when installed significantly higher than the protected object. In case of a lightning mesh this condition is neglected. On a flat reinforced concrete roof, it is only a few centimeters above the grounded metal reinforcement in the slab. Lightning simply does not "notice" such a difference in height. Therefore, reinforcement and mesh take almost equal number of strokes. In this case, the grounded reinforcement plays the same role as the grid: the lightning current flows through it to the grounding conductor and further to the ground.
ENIN Institute to the name of G.M. Krzhizhanovsky in Moscow carried out the calculation of lightning strikes into a building with a flat reinforced concrete roof with the dimensions of 40 x 40 m. The simulation was performed for buildings with the height of 10 to 60 m. The result: in 35–40% of cases, lightning hits the fittings passing the mesh. The situation can be modeled also in the ZANDZ lightning protection service. In order for the lightning protection mesh to protect from a direct discharge, it must be raised above the roof to the level of 3–5 m. Then the mesh will function as a closed cable lightning rod, but compared to them it will be more cumbersome and expensive
Metal mesh on a flat reinforced concrete roof will help to secure technological and electronic equipment on the upper floors - residential or office. If there is such equipment, then it is necessary to weaken the influence of the electromagnetic field of the lightning as much as possible. The mesh is foreseen specially for that by AD 34.21.122-87 standard - not to protect against direct impact, but as a way to improve the electromagnetic environment in the building. Practice shows that it is extremely difficult to convince the State Technical Supervision Authority in this interpretation of the standard. Therefore, lightning protection mesh is designed anyway on a reinforced concrete roof.
Learn more about the protection features of the roof and the use of a lightning protection mesh in the recording of the webinar of Professor E. M. Bazelyan.