Technically, if we were to bind the logs together with weights to have negative boyancy and dump them into something like the Mariana trench the lack of heat, sunlight, and a fair bit of microbial action should drastically slow decomposition. Especially if they are treated/coated with something. Its why we can still find old wooden plank ships at the bottom of the ocean.

But I'd imagine that the amount of trees we'd need to dump into the ocean to try to lock away the extra carbon in the atmosphere might (and I say might because I'm not in any way qualified to speak with authority about this) be such an terrifyingly huge amount that the lower rate of decay wouldn't matter due to the sheer volume that we would need to be storing in the ocean. (Not even accounting for accidents or failures of our systems that wound up with the trees breaking free and floating back up to the surface.