Before we moved, I used to bank fish it all the time. Never saw a single kayak though that has changed recently after a kayaker petitioned management out there to allow it at a reasonable fee. Honestly, I thought he had no chance to convince them to do it.
So, yes, fog is a big deal on certain days, many winter days, of course, when the air temperature is greater than the water's. For that reason, at least on those days, you just can't take a kayak out in the depths and would be forced to hug the shoreline for reasons of safety. The boats out there run a full open throttle going out and coming back in more than on most lakes. Even on days when the fog is a thick as pea soup, I have heard (can't see them) boats racing out toward the dam area.
Another issue? It is an extremely windy lake most days with a noticeable wave action. It'd make kayaking an issue for all but the most experienced. Even up on the shoreline where I used to fish, the waves sort of slam the banks. You have to get back in the coves to find anything resembling calm water. I bring this up because even if you stay shallow, it won't necessarily be calm and you'll likely rock and roll a good bit.
A third issue is it has a big complement of boats on it most days, especially winter months.
Anyway, if you take your kayak down there, I think they limit any launching to the boat ramp area only but you could slide into the water just on the edge of the concrete. I saw a photo of someone who beached his kayak along there.
I think I'd launch, cross the little cove at the ramp area, hug the shoreline and work along it and paddle/pedal up into one of the north feeder creeks. This, anytime during the winter. For summer months when the water gets 90 degrees plus, the boats largely go to other lakes and you could have a blast catching tilapia up in the same feeder creeks (north side of lake). You could also work down to the south, again following the shallows and big bass are still caught down there year-round.
I'm not sure now but just a few years ago, they had fishing tournaments almost every week and it usually took 25 plus pounds for a 5 bag limit to win or place. It's an impressive lake for LMBs for sure as that 5 lbs. plus average weight in tournies shows.