Big Red Rooster :
I own a GTX 970 (the EVGA SC ACX 2.0 variety). Non-overlocked. If, for instance, I were to apply a closed-loop water cooling system to it, would I get increased performance? If so, how much?
It depends, get software that monitors stats of your card whilst gaming. MSI Afterburner is an excellent free one. Keep an eye on the GPU clock frequency and VRAM speed. It is known that many cards start to slow themselves down once they reach a certain temperature. So if your notice the card down-clocking itself then yes more/different cooling will help. But, to be honest the amount you spend on a water cooling loop will be better kept and used towards an upgrade later next year when you sell you existing card.
Another thing to consider if your card is down-clocking when under heavy usage after a few minutes is case cooling, for instance I have a Sapphire R9 290 (Tri-X) and have a 120mm case fan blowing air directly from outside the case onto the card to feed it a constant supply of fresh cool air. It never gets above 74degrees and never down clocks. Though I'm 'lucky' to live in a country where it is generally cold so cool ambient temps are a bonus for me.
I've only ever overclocked one graphics card (7800GTX) a few years ago and for the extra 4fps I was getting in some FPS games was not worth the hassle of horrible fast and loud fan speeds along with graphics glitchs and random crashes. I can't remember the figures but it was only a small overclock, something like 4% but was a disaster.
The only other thing I've noticed with card performance is dust. Over time the card fans gather dust and gradually degrade the cooling performance of them. Air in a can or cotton wool buds and a vacuum cleaner will clean them up well and can fix performance issues.
What games are you wanting that extra little performance from because often tweaking the graphics in the game setting can be the difference between 40fps and 60fps!