This article is from the Final-Fantasy and other Square Soft Games FAQ, by email@example.com (Nick Zitzmann) with numerous contributions by others.
Seemingly, no; but it can happen.
When Ayla reaches a particularly high level (like level 70 or so), her
Fist gets upgraded and hits harder.
This may happen several more times - up until Ayla reaches around level
98 or so, and has the game's ultimate weapon in her fists. Now, she can
punch an enemy, and if it's a critical hit, it's always 9,999 HP damage!