Okay, I am still very new to the game in comparison to the majority of those reading this. 

I am currently maining a Dosa and absolutely love it , I know awakening will be out soon and  I can not wait to try it. (Probably will just stick with suc as it is so damned good)

However,  I do have a slight concern to address. AP.

As it stands at the current moment, we have the Marnis pocket watch. Has no raw AP on it, but hidden AP  

Now when we are able to have regular AWK weapons (like a blackstar  or something) It will not only have the same hidden AP but the static raw AP as well 

If you've played a Dosa or fought against one, you know that already, we have some insane damage. 

Will this be addressed or... will Dosa kill most mobs and PVP in one shot?  I think actually this is what is taking so long to release Dosa Awakening 

That is not really a concern.

When you play succession, 70% of your mainhand AP and 30% of your Awakening AP get added together in order to calculate the AP used for prime skills. This is done in order to make sure you cannot just fully neglect the awa weapon enhancements. However, all additional effects, like monster AP, species damage, crit damage etc on the awakening weapon get applied fully.

When a class doesnt have their awakening yet, 100% of the mainhand AP is instead used to calculate the AP for prime skills. So you basically already have the same AP as you would have even with an awakening weapon equipped (potentially more, if your awkening weapon is of a lower enhancement level in the future). In order not to forget about the additional effects on the weapons, the pocket watch was introduced (basically giving you back the species damage, monster AP and garmoth heart effects you have on awa weapons normally).

So no, getting an awa weapon will not increase damage for succession classes. The calculation applied makes sure that it is not in addition to the AP you already have through your mainhand