How important is the order of Vertices in the mesh array that the triangles point to?

Simply put does the order of the Vertices are set in the array matter... [I know the order they are referenced in the triangles is important but what about the Array of Vertices?].

To clarify if its not clear... is one better then the other [Imagine this array has 1000's of vertices instead of 9]

 0-----1-----2
 |    /| \   |
 |  /  |   \ |
 3-----4-----5
 |    /| \   |
 |  /  |   \ |
 6-----7-----8
        

 0-----8-----3
 |    /| \   |
 |  /  |   \ |
 5-----6-----1
 |    /| \   |
 |  /  |   \ |
 2-----7-----4
        

I am trying to think out or learn how to make a custom mesh and as I build the mesh swap out sections with a predefined mesh/array of vertices ... E.G. a 3D Tile map...(there is a possibility I will end up using sub-meshes for each tile but I also don't know or understand if that would have a large effect on performance ether.