The Beatles never recorded through any Neve console... There was a Helios at Apple, but I don't think they ever got to record through it. Trident had a Sound Techniques, which was kind-of like an API, tonally - agressive.
The last console they used was a transistorized REDD and Geoff Emerick complained he could never get the drum sound he really wanted out of them.
The REDD tube consoles were completely different from later Neves. Neves were much more open sounding - the REDD tube consoles had a kind-of "pinched" low-midrange with a bright top-end, which I blame on the preamps. I have a couple V72 preamps that sound just like it when driven moderately hard.
Maybe it sounds like some console, but to say it sounds like an OD'ed Neve is a bit of a stretch.
The MCI 400 series had a squishy sound when overdriven, maybe that.