Demodulation of direct sequence spread spectrum technique
If your symbols are much slower than the carrier or spreading rate, say 1000:1, then a precise correlation (aligned both in code bit and code edge phase) followed by lowpass to drop system bandwidth by 1,000X, will indeed drop the noise floor by 1,000X. Done it, liked it. Even injected a strong tone, to attempt to block; up to limit of linearity of the mixer in the correlator (I used a MC1596 multiplier) the blocking tone was spread out in spectral occupancy and as expected the desired energy was de-spread.

Thus for 1,000:1 despread, expect 30dB improvement in SNR.