Will I destroy decent trainers duathlon training

You ride way faster with clip-in pedals.

If you don't wear them, you're going to have a huge disadvantage in the race.

I'm training to join training with a triathlon club.

I won't be challenging anyone, they're absolute monsters.

At the moment I'm a lot fitter than I am fast. Ie always backing off through bends, downhills etc.

Clip on shoes won't make me faster at the moment, confidence and experience will.

The clip-in will make you a better, more confident rider. You will feel as one with your bike and being locked to the bike makes a big positive difference in handling at high speeds.

Riding with running shoes is like having a full fuel belt and water pack for a 5k. Not only is it slower it also signals you have no idea what your are doing.

Of course it's possible. I've done it without a backpack. If you're on a triathlon bike, just bungee the running shoes underneath the aero bars. If it's a road bike, it's still doable. You can buy a rear cargo rack that mounts to the seat post and bungee the shoes on it. I have one that mounts only to the seat post and weighs less than a pound. It costs less than $20. Here's the first one I found on Amazon.

You could even put the toe of each shoe into your two water bottle cages and bungee them in place so they won't fall off. To carry your water bottle, you could then buy a water bottle cage that mounts behind the seat.

Do a time trial on the bike with running shoes and then do the same time trial in clip-in cycling shoes. You will be a lot faster. This is pretty basic cycling knowledge. Look it up online.

Here is a simple example. Without clip-in shoes, you're only able to use one leg at a time to go up a hill. With clip-ins, you can use both legs, pushing down with one leg and pulling up with the other.

Plus, you won't need to carry your running shoes in a duathlon. Most duathlons are run-bike-run. You run to the transition area, change shoes, do the bike ride leg and come back to the transition area, put your running shoes on and do the final run leg.

I'm lucky I have access to the full duathlon course. I realise in events there's somewhere to leave shoes

I like the idea of bungee cording, but someone could steal my other shoes when I'm running and bike is locked

I am clueless, I've only done 7 rides and haven't had a bike in decades. My pedals have got holes for clips

It also seems to be a basic cycling myth. People who actually tested power output with and without clips found the difference in power output is negligible if any at all. Which is somewhat logical, if you think about it. Your most endurance oriented muscles are pushing, not pulling. You can probably get a bigger power spike with clip ons, so it might be important for sprinting.