The center of the cell in this case is a way to say "the nutrients arrive to every part of the cell", and should not really be taken literally as "the center". If the cell is modeled as a sphere, with the nutrients diffusing in from the outside, the whole sphere would be filled with nutrients when the nutrients "arrive to the center". Figure 1 shows how the nutrients would diffuse from the outside layer further in. It is like saying the whole glass would be filled when the water "arrives to the top". It does not particularly mean that the vital organelles are in the center, but is just used to illustrate the fact that nutrients diffuse into and can reach all parts of the cell.
Figure 1: an illustration to show how nutrients would diffuse from the outside to the center of the cell, filling the cell with nutrients. This image is trying to model a cross-section of a circular cell. The nutrients would for example enter from around the green layer, and gradually get to the middle/center dark blue area.
Resources may get depleted before they reach the "center" of the cell because of the rate of diffusion, and also because metabolic processes may convert the resources into other molecules (e.g. converting glucose into ATP; glycolysis happens in the cytoplasm, and can happen in any part of the cell. If that particular glucose molecule is used up, then it will not be able to travel to the center).
Moreover, the "important organelles" are not in the center in particular. If you have seen an image of a typical plant cell for example, most organelles are around the walls of the cell (Figure 2).
Figure 2: a typical plant cell electron micrograph.
Also, you must remember that the Surface Area to Volume ratio is also a restriction for the effective diffusion of waste substances out of the cell. The small volume / big surface area is not only because nutrients have to diffuse in, but also because waste products (like CO2) must be able to diffuse out of the cell, through the membrane.
