seeing as I don't play OTB, nor am I "training" for it, I just play CC, and depending on my mood and the will to win, I will use opening books, databases, and of course Notepad and the analysis board to look 8-12 moves ahead. **
CC chess, IMO is the aim for perfection, Duboius and "pychological" play won't get you far, but solid idea's, tactic's, openings and stratgedy will.
Also, CC is a great opurtunity to learn ---In my CC games I will often find myself playing complex endings, And because of the amount of time I have, i'll go off and read a chapter in a relevant endgame book, then move - hence, I learn.
And I somewhat doubt the use of the analysis board is detrimental to visualization skills, I should imagine it neither harms or helps.
**most of the time I simply can't be bothered to do that mind.