Is it practical to use relay contact resistance as a shunt?

It depends what you want to use the voltage developed across the shunt for.

If you want to know the current direction, then yes.

If you want to know the magnitude of the current, even to within a factor of 10, then no. Relay contact resistance is far too unstable to be predictable. It will change with every relay operation, with ageing, with contact erosion, and probably with phase of the moon ;-).

If you want to cheapskate on a shunt resistor, then use one of the leads between the motor and the relay, with Kelvin connections. There the main error will be the temperature coefficient of copper, about 10% variation for each 25 °C change. This will be easily accurate enough to discriminate stuck from operating. I used 300 mm lengths of 1 mm² copper wires as current shunts in my final year undergrad project.

Not really, the relays contact resistance is succeptable to wear and vibrations.

Eg: this datasheet claims 100mΩ max. but doesn't say how low it might be.

I measured less than 3mΩ here (11mV@4A) but as the relay ages I expect that may increase to as much as 100mΩ before the end-of life of the relay. End of life being defined as when the relay no-longer meets the datasheet specifications.