Makes no odds how thick the wall of the tube is. Once something penetrates the tyre there's no way on earth any inner tube will resist it. You may buy time with one particular brand over another, but you're talking yards rather than miles.
Punctures tend to come in batches and if one of those spells coincide with the purchase of a new tyre or tube it's tempting to blame those. 99% of the time it's just luck, your number came up and that's that.
I find that if I use a heavier tube, I can buy quite a lot of extra time, at least sometimes.
The trick is that the heavier tube is a larger size, rather than necessarily being thicker rubber (eg a 700x32-45 tube in a 700x28 tyre). If you use an oversized tube, it's not stretched, which makes it much harder for something sharp to cut it, and if it's a thorn, the tube can seal around the thorn, which plugs the hole in the tube quite well,
A bit of glass or flint can take quite a while to get through an unstretched tube, allowing me to get home by pumping every few miles, and a thorn plugged hole may allow 2 or 3 days before needing to pump.
By contrast, using a lightweight 700x18-25 tube in the same 700x28 tyre will more or less guarantee prompt and complete deflation as soon as anything sharp gets through the tyre, even by a fraction of a millimetre.
The exception to randomness when getting repeated punctures is when your tyre is about to wear out. With slick tyres, it's difficult to tell how much life is left in the tyre.
