How does sideslip indicator react during crosswind?
1. Answer to original OP

In a stable airmass, the amount of sideslip/skid indication is irrespective of the wind strength and orientation; it is a function of the relative velocity of the airplane against the airflow only (stable winds are referenced to ground). That is, with all engines operating and rudder centered (assuming no inherent asymmetry), then the sideslip indication will be zero, whether you have winds or not.

In gusts, the winds are transitory against both the ground and the airplane frame of reference, which will induce change in airspeed, AOA and sideslip. This will result in change in aero forces and moments, until the inherent stability of the airplane stabilizes the airplane or the gusts die down.

In a pure lateral gust, this translates to a sideslip (and an increase in airspeed) measurable on the yaw string, and generates a side force measurable on the skid indicator.  Both would concur in measurement (opposite in visual direction).

2. Addendum to address the modified OP


  The air mass is no longer an inertial frame of reference.


No one ever uses airflow as a frame of reference unless you're doing fluid mechanics, which is not very relevant here. Airflow matters to airplane only because the latter responds to airflow changes (via aerodynamic forces).

The ball does not measure the crab angle; it's dumb and doesn't know what the airplane heading is or where it's going. The ball only measures the side force relative to the aircraft, much like a bubble level. With all engines operating (or no engine operating) and in flight, only aerodynamics can generate side force, most directly via sideslip (control surfaces can, too; but the magnitude pales in comparison).

In your scenario of a linearly increasing crosswind, sideslip increases with crosswind, measurable by the string. Increasing sideslip induces side force, measurable by the ball, whilst pushing the airplane off course, further increasing crab angle. At the same time, the airplane yaw stability responds by yawing the nose toward the crosswind. After some time, without pilot correction, the airplane has yawed sufficiently that the crosswind becomes a head wind.