No, the result of increased wealth inequality, even if you maintained the same level of social mobility, will worsen not improve situation. The description of a rise in absolute mobility would be a misunderstanding of the issue.

If that is too theoretic, consider the analogy of a lottery where one group of children win automatically and an other group has say a 10% chance of winning during their life. Increasing the prize (i.e. a rise in inequity among classes) serves only to worsens the situation not only for the median and average members but the vast bulk of the lower class since those who don't rise (the vast majority) are now even worse off relatively.

Or indeed by your logic simply raising the salary of a CEO by a massive amount also raises the "absolute mobility" of all other employees

So unless mobility also raises by at least a corresponding amount, any worsening of inequality at birth will only worsen the situation by every meaningful standard. And even then it is probably a bad idea.