Yes. All of his stats will effect on all provinces he rules. Some of his V&V also have global effect. Just bring up his stats page (right click on his unit) then place the mouse over the stat, you should be able to see the details and how it will effect the population.

I believe that the acumen effect is calculated as percentage. 50% of 100 is less than 10% of 1000. So, the bonus is near negligible when the income is small but you should see a big increase when the economy is developed well enough.