Coloured Labels. Is it possible to....

No.

apple-lovin-it wrote:

make a certain file extension adopt a certain label colour system wide without having to do each one seperately using the "Get Info" menu

If you'll settle for "in my Home folder" rather than "system-wide", I think there's a way to do it. Restricting the scope to your home folder avoids any write-permission issues or search limitations.

Click on the house icon in the sidebar, and then from the Home folder window hit "Command-F" to bring up a search. Set up the search location as the current folder rather than "This Mac, search for "File Name" rather than "Contents, and then enter the desired extension in the search box. For pdf files in my "testaccount" Home folder, the search would look like this:

Next click inside the window with the search results, type Command-A to select them all, then type Command-Option-I to bring up the "Inspector", a multi-item Info window. From there you should be able to change the label color for all the selected items: