How difficult it is to record a string section or choir depends on whether there are featured instruments. Otherwise you can set up a simple stereo pair, and record the whole lot at once. Moving instruments/singers to achieve a balance. Even if there are featured instruments, I would expect that a skilled recording engineer with sufficient equipment could set up microphones and achieve a reasonable sub-mix in an hour. They wouldn't have to record as a huge multi-track even if they did have individual mics. They could do a sub-mix through a mixer, and only record the (say) two channel submix.
If they did use stereo pairs then they would get some room sound on the recording: more than if they used individual microphones. However, I suspect that Neil is not going to be too worried by that.
Can I make it clear that I'm not suggesting that they should do this. I'm just discussing the plausibility of getting a reasonably good sound with the recording strategy that has been described.