VAOs act similarly to VBOs and textures with regard to how they are bound. Having a single VAO bound for the entire length of your program will yield no performance benefits because you might as well just be rendering without VAOs at all. In fact it may be slower depending on how the implementation intercepts vertex attribute settings as they're being drawn.
The point of a VAO is to run all the methods necessary to draw an object once during initialization and cut out all the extra method call overhead during the main loop. The point is to have multiple VAOs and switch between them when drawing.
In terms of best practice, here's how you should organize your code:
initialization:
for each batch
generate, store, and bind a VAO
bind all the buffers needed for a draw call
unbind the VAO
main loop/whenever you render:
for each batch
bind VAO
glDrawArrays(...); or glDrawElements(...); etc.
unbind VAO
This avoids the mess of binding/unbinding buffers and passing all the settings for each vertex attribute and replaces it with just a single method call, binding a VAO.