Does multipath apply to sub-1kHz signals?
Disturbances in the EM field due to source oscillations propagate at the speed of light (3e8 m/s).

For a 1kHz (300km wavelength) signal received at 10m, and assuming a very conservative worst case delay path of 40m, the worst case multipath delay will be (40-10)/(3e8) = 1e-7s (100ns) in time.

Assuming a sinusoidal wave with amplitude A (and also therefore max derivative A), the maximum signal inaccuracy will be 1e-7*A/A = 1e-5% = 100ppb.

These calculations do not take into account the constructive/destructive interference of multiple multipath components (not sure how to estimate that?), but overall, the worst case time delay (100ns) and inaccuracy (100ppb) delay for a given multipath component seems negligible.