- Not unless ESD event occurred which being CM insulated, makes it a susceptible target.
Otherwise floating battery powered Diff Amp works fine, then use optical or digital or magnetic isolation for output to data collection system.
The CM gain can be computed by the (series leakage to input shunt )resistance ratio * the tolerance error of the matched R's * differential gain. Coupling from Common Mode noise sources can be a problem if cables and R matching is not perfect as CM noise tends to be orders of magnitude large in E fields e.g. 10V/m from powerlines than the differential signal but also much higher impedance. So a CM shunt connection of grounds reduces this somewhat.
The environmental reasons for isolation depend on each application affect the solution. e.g. HV, safety leakage, RF immunity etc.
Sometimes a choke is used to get low f grounding but improved RF isolation.
Sometimes an RC connection is used for ground connections.
Sometimes an active CM signal is used to active guard the shield or use as a remote ground and only receiver ground connection is used for a shield. This is standardized as "Right Leg Drive" in patient monitoring.