Is it Essential to Root a Nexus Device in order to Customize or Personalise it to your liking? My understanding is that rooting an android smartphone or tablet allows you to add functionality and to flash custom ROMS (amongst other things) like MIUI or CyanogenMOD.

A Nexus device offers the pure "vanilla" android experience from Google without the additional "skins" etc. that mobile phone companies add/tweak to further differentiate their product from one another.

If it is the case that nothing has been added/tweaked, customised etc. on a Nexus 4/7/10, can I achieve this personalisation (via the Google Play Store) on such a device without the need for rooting?
If you're not sure if you need Root, you don't need Root.

There are any number of alternative Launchers you can install that will give your device a custom look-and-feel and add/adjust functionality from Vanilla Android. Heck, there are Launchers that can simulate the look-and-feel of iPhone and Windows Phone.

Have a look on the Play Store for "Launchers" or "Home screen replacements".