Anything is fixable.. cost is the killer.
I brought my second GTI at just under 140k and I can't say it doesn't drive any worse in the slightest to my first mk5 GTI at 49k. I did also replace the cam follower, cam chain & tensioner.. timing belt, water pump etc. :)
Unfortunately, these engines do have a tappety type sound anyway from the injectors. but if its over exaggerated and very diesel sounding then your cam chain and tensioner will need doing. by the sounds of it, you're in the same position as me - had budget left over! so it makes sense to get it all sorted now with the spare cash