File type icon colours

We're currently designing a new "Document Management" feature for our application, and I've come to the part where I need icons for the file types. I've gone down the route of doing something custom, but the question has come up "Do we need them to have colours or should we go with plain (likely grey) instead?"

These are the icons I've got so far. The logic I've gone with, is that users have become accustomed to the icons of the applications they use, and therefore the colours of these icons roughly reflects the icons of those associated applicattions.

For comparison, here's the grey variation

Is this something that is important, or does it not really make any difference? I'm looking specifically at a document listing, so there may be hundreds of lines in a table so the icon may/may not be the fastest way for a user to determine what type of file it is.