It depends on the rig and the system as a whole. The more help your TT needs to sink vibations away from the record and/or the more resolving the system, the more difference you'll probably hear.
On my Teres 265/OL Silver, a ring made a sonic improvement on all records. In truth, flattening warped records was a side benefit. The greatest benefit came from the ring's ability to help the platter absorb and reduce vibrations from the stylus-groove interface. Using it produced a consistently lower sound floor... less mud, greater musical and sonic clarity.
Again, YMMV depending on circumstances.