Lets define a few terms first....
Trim tab - an adjustable tab (in flight or manually on the ground) tab used to move a control surface in a direction we desire (to induce a trimming force).
Servo tab - a controllable tab used to move a control surface. I a sense a trim tab is also a servo tab, but servo tabs (by name anyway) are typically considered more of an active control function. Some large aircraft built prior to hydraulically boosted controls had servo tabs connected to the control system. The control system moved the servo tab which in turn drove the main control surface to the desired deflection (I think the B-29 was one airplane controlled this way).
Anti-servo tab - A tab whose movement is used to counter the movement of a control surface. This is typically done to artificially induce control force / feed back.
The RV-12 has an Anti-servo tab. It also functions as a pitch trim tab by having an adjustable neutral point, but that is a secondary purpose.
With a horizontal stabilator with the hinge point somewhere close to the center of pressure (as we have on the RV-12), there would be nearly zero control force / feed-back without the anti-servo tab. The anti-servo tab adds artificial feed back force by deflecting in a direction that tries to move the main surface back to neutral when it is moved by the pitch control system. That is why the tab constantly moves whenever the stabilator is moved.
In a nut shell.... if the anti-servo tab was non functional you would have little to no control force in pitch, which would probably make the airplane challenging to control.
I think a future release of the POH is going to cover recommendations for dealing with this. I think the primary one is to induce a different trimming force (deflecting the flapperons) that would then allow you to work the stick against the control force induced by the trimming input. It would be very similar to flying an airplane that is out of trim in pitch.... to change pitch you increase or decrease the pull force on the stick but it never gets to neutral/zero.