No, for during the time the light takes to get to the central observer from the front, the train has moved closer to where the front bolt was and farther away from where the rear bolt was. Hence the front flash travels a shorter distance than the rear flash. The observer in the train then notes that the front flash arrives first, before the rear flash, and both flashes have traveled the same distance in the same time. Thus the front flash must have occurred first and the rear flash later. The flashes are not simultaneous in the train system.
Simultaneity is relative.
Notice that the reverse situation, in which the train observer sees the flashes as simultaneous would lead to the platform observer disagreeing. Simultaneity is relative. One thing which is absolute is the displacement measured perpendicular to the direction of relative motion. From the symmetry of the situation and the first postulate, if the moving frame had shrinking transverse dimensions and permanent marks were made on the y axis, say, then the opposite view was adopted, the marks from each situation would be separated, and we could tell which system was in motion , contrary to postulate 1. The gun and bullet analogy is a good one to understand this symmetry argument.