The USN always flew ASW CAP off of CVs from the earliest days of the war (easy to check in Lundstrom). This is possible because they can take of and land while underway. The IJN seems to not have done this, at least not as much. Their ready CAP was usually fighters (sensible), but since they frequently had no, or bad, radios, they'd not be much use for ASW (they also carried no bombs).
As for floats planes, that's tricky as well. If they expected combat, sure, they'd cat off the floats, but the problem with this is recovery. The CA (or BB) has to stop to pick them up, which leaves them vulnerable to subs. SH4 can't really deal with this aspect of flight ops (it doesn't deal with flight ops for CVs well, at all, either—not just on a compulsive accuracy level, but in terms of what you see as a player. You'd simply not ever see so many planes buzzing around, if they were airborne off a CV, it would be because they were going someplace to attack).
Personally, I'm using a mod that uses cloned planes with VERY short range for the CVs, and only has 1 or 2 per CV. For the IJN even this is likely overkill.
I think for the most part, you'd only see BB floats in anticipation of combat as gun control spotters (I believe this was their purpose in IJN doctrine). The specialized CAs like Tone and her sisters (later Mogami) might have been a different matter. They clearly were used to fly search patterns for the enemy. There's the rub, though. The whole of IJN doctrine revolved around attacking Fleet units. ASW was considered "defensive", so they'd likely not "squander" floats on ASW patrol—they'd be holding them so that when they caught word of the enemy, they'd be ready to go.
My best guess would be that you shouldn;t see CA floats on ASW patrol, ever, or at least very very very rarely.
tater
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