It will work okay, in fact series resistance will be near minimum, but leakage will be relatively high (perhaps in the few uA range) increase at high junction temperature (perhaps >100uA at Tj=100°C) due to forward biasing the isolation diffusion junctions and input protection diodes.
The transmission gate resistance will typically be more than 200\$\Omega\$ (more at higher temperatures) so error could typically exceed 10% at Tj=100°C even if the source is low impedance.
If that's unacceptable (and keep in mind that higher negative voltage can damage the chip should excess current be allowed to flow) you might want to consider a charge pump such as the TC7660 or ICL7660. An 8 pin package plus two capacitors are all that is required.
Since the CD4051 (unlike the 4016/4066) includes input level shifters, you can simply connect the 0/5V control inputs directly. That is my recommendation if you need to accurately pass signals of -300mV over a range of temperature.