No, sometimes it will make it worse.

Heteroskedasticity where the spread is close to proportional to the conditional mean will tend to be improved by taking log(y), but if it's not increasing with the mean at close to that rate (or more), then the heteroskedasticity may often be worse.

[![plot of two data sets, one with spread proportional to mean, which shows improvement when taking log(y) and the second with spread going the other way, which gets worse after taking logs][1]][1]


  [1]: https://i.sstatic.net/8dzVP.png