FWIW this is how almost every communication system works. They're all weaker than background noise (e.g. sunlight) but you extract them by correlating with some kind of carrier signal (often but not always a sine wave)
You do generally need a tuned filter before the rectification, unless you have an extremely large signal dominating the local airwaves. Which is precisely the parent poster's point: with RF you are almost always doing something to demodulate the signal. Whether you are doing it with a sine wave or something more complicated is not that fundamentally different. (and if you're looking at a spectrum analysis, that is looking at the radio signal from the point of view of that sinusoidal modulation scheme, so you will see such signals 'above' the noise floor more readily than something using a different modulation).
I'd argue that "correlation" is an accurate description of what you're doing with Gold codes - you're testing the known sequence of the output of a PRNG against the received signal, and only accepting it when the data correlates, otherwise you're adjusting the offset and trying again until you find a high correlation (strong +ve and -ve spikes) or you give up and assume there's no transmission. There's nothing in the received signal that tells you there is a real signal there at all, without correlating against every possible offset.
If you compare that to the majority of radio transmissions modulated on a sine wave carrier, there is a clear signal there and you don't need to correlate anything to tell you that, and you don't need to keep trying different offsets - you can just demodulate using a carrier of the correct frequency and the result is correct, just with a slight phase shift relative to the local carrier and which probably isn't even relevant in the frequency domain of the signal.
The key point to me is the trying repeated offsets to try to pick out a signal well below the noise floor, and choosing the offset that provides the best correlation, compared to demodulating a very strong signal that's obviously there by just adding a carrier. The latter could be done using "correlation" if you're implementing an SDR, but it doesn't have to be, and most radio hams would prefer to think of it as a simple analogue operation instead.
A strong signal 'that's obviously there' is only obviously there after you've already filtered it to some extent. If you were to look at the raw broadband RF environment on a scope you very much would not see the vast majority of signals there. And when you're demodulating you do often need to tune the phase and frequency of the carrier you're demodulating with, as well. GNSS signals are just generally quite low bandwidth and so that process takes a while.
Not to say that such codes aren't a neat trick, but it's useful to consider that these are in many ways the same thing.
No, conventional radio broadcasts can be received with a low noise amplifier and a tuned filter.
The received GPS signal, at ground level, is lower than the thermal noise floor. And the 1.023MHz code is modulated on the RF carrier anyway.