Working on log pressing will make you better at log pressing in the same way that my Olympic lifting will make me better at Olympic lifting: assistance exercises support these competition lifts.
So, if you want to get stronger a log press will help to a degree, but I think the best movement for overhead strength is probably as strict a movement as you can get. A log press is designed as an awkward lift to test a bit more than outright strength from the shoulders... notice the backward lean seen in a lot of strongmen as they recruit more than just the shoulders and enhance the stretch reflex? Same for the 'Olympic press'.
If you want better overhead weight handling, a better exercise is probably the push-press. However, as Delvis points out, if you want to do log pressing, work it into your programme at some point.
So, if you want to get stronger a log press will help to a degree, but I think the best movement for overhead strength is probably as strict a movement as you can get. A log press is designed as an awkward lift to test a bit more than outright strength from the shoulders... notice the backward lean seen in a lot of strongmen as they recruit more than just the shoulders and enhance the stretch reflex? Same for the 'Olympic press'.
If you want better overhead weight handling, a better exercise is probably the push-press. However, as Delvis points out, if you want to do log pressing, work it into your programme at some point.