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Stability is primarly discussed in small signal analysis. As you'll know, it uses a simplified linear OP modell and doesn't care for signal magnitude. Thus it can't answer your question.
When advancing to large signal analysis, you have to notice the various nonlinear effects of a real system.
To consider a simple case, the OP might show an almost linear characteristic until the output voltage is clipped near the supply rails and no slew rate limiting takes place. If the circuit oscillates at all, the oscillation magnitude will raise then up to the supply limits. Strictly speaking, the loop gain must be slightly larger than unity to get an increasing oscillation magnitude. For more complex OP characteristics, the real behaviour won't be easily to predict.
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