I have not tried that but I share your frustration with punctures. While I think it would provide some small degree of protection, I don't see it being much of a fix. I suppose it will stop a few punctures, but anything that gets into the casing of the tire and can puncture the barrier tube can also puncture the air holding tube. I'm not saying not to try it, by all means. Please do so and report back with your findings.

As for me, I've gone tubeless on a couple of my wheels and that works fantastic for puncture resistance. But it creates a whole new set of problems with rim tape and sealant issues. Not to mention the initial cost if you don't already have tubeless ready wheels and the tubeless capable tires. Living in the desert, sealant can dry up in a week or less if I'm not using the bike. Of course, the nice thing about tubeless is that it's just another option. You can run a tube on a tubeless ready rim and tire if you need. In fact, I learned the hard way to always carry a spare tube for those instances when you have tire damage beyond what the sealant can repair.

Another option is a premade tube insert to do exactly what you're trying to do. These inserts are made of a more durable material than regular butyl rubber. I tried this once but it was a colossal failure because I could never get the insert to stay in place when mounting the tire. That could be my procedure or the brand/type of insert I was using, I do not know which.

And yet another option are more puncture resistant tubes and tires. I have tried this also with good results. The downside is greater weight and rolling resistance due to the heavier construction. But for training rides, that's almost a good thing.

Between the various solutions, I like tubeless best because I can run a little lower pressure for more compliance and a more comfortable ride. But as mentioned, the downside is increased cost and maintenance, particularly in the hotter months. I think the puncture resistant tubes/tires is the best financial compromise as they don't require specific wheels and can easily be swapped out on race day if you're competitive.