While I am designing my web design company's new site, I came up with the thought of using Ajax somewhere in the pages, so it shows we are trained in it. 

But then – I thought "hang on!" – am I just using it for the sake of using it? Will it add actual functionality to the website or will it just annoy?

I haven't even thought of where/how to use it! I'm undecided, but I just wanted to make the point of "don't just use it because it's there". Use it because it will enhance the quality, usability or functionality of the site!